#I believe the answer is Yes if the DM accepts the Forgotten realms Lore about Kiltzi in 5e
Otherwise nothing can be said about it.

As for canon Sune, Sheela Peryroyl, Freya, Aphrodite and Hathor are probably goddesses you should check.

The Forgotten Realms Wiki is the source of my deduction (1991) but there is no other info for 5e according to Please stop being evil so that would be the DM's call:

If the DM accepts the old info here is my interpretation of how it should be handled now in 5e:

Kiltzi was the Maztican goddess of love, both romantic and lustful, fertility, and health.

As Niv Mizzet points out in his answer she is the goddess of love (both romantic and lustful) and the gender of the people in love should not matter.

ET got home's answer does a fine job at suggesting how to handle it in 5e.

So for that part I would say yes.

(...)her favored form of devotion was performed privately between a man and a woman.

Favored means she prefers love between a man and a woman, not that it is exclusive as far as I understood. It makes perfect sense that she prefers it to be between a man and a woman because she's also the goddess of fertility!

If you're the DM you decide (go for it!), if you're not, ask the DM how he/she/whatever rules it.

Sidenotes:

1. Since the goddess Kiltzi is not in the 5e edition this question probably shouldn't be tagged with the 5e edition, because if your DM accepts she's in 5e, she could be either way the DM want or she could follow the Forgotten realms Lore, so that makes it difficult to answer the question with a satisfactory result for the community. The Default answer is ''she's not in 5e''

2. As for 5e Canon, there is no answer as pointed out by Please stop being evil

3. Sune,Faerûnian greater goddess of beauty and love. and Sheela Peryroyl are in 5e so perhaps that's there you should look for (Forgotten Realms).

4. @Dan B suggested adding Aphrodite and when I searched for her I also found Freya and Hathor.

5. More info in:Love Domain

   There are three deities whom after the Spellplague lay claim to the love domain. One of them was Sheela Peryroyl (...) Sune, was the second deity whom called to her followers to find and collect beauty in all forms and things. Love must be shown daily. Many nobles in cities followed the teachings of lady firehair who thrived on her followers love(...)And lastly there was Kiltzi the Maztican goddess of love, lust, and fertility. (...)

6. This Question can give you more info:How common is homosexuality in the Forgotten Realms?

I believe the answer is Yes if the DM accepts the Forgotten realms Lore about Kiltzi in 5e

Otherwise nothing can be said about it.

As for canon Sune, Sheela Peryroyl, Freya, Aphrodite and Hathor are probably goddesses you should check.

The Forgotten Realms Wiki is the source of my deduction (1991) but there is no other info for 5e according to Please stop being evil so that would be the DM's call:

If the DM accepts the old info here is my interpretation of how it should be handled now in 5e:

Kiltzi was the Maztican goddess of love, both romantic and lustful, fertility, and health.

As Niv Mizzet points out in his answer she is the goddess of love (both romantic and lustful) and the gender of the people in love should not matter.

ET got home's answer does a fine job at suggesting how to handle it in 5e.

So for that part I would say yes.

(...)her favored form of devotion was performed privately between a man and a woman.

Favored means she prefers love between a man and a woman, not that it is exclusive as far as I understood. It makes perfect sense that she prefers it to be between a man and a woman because she's also the goddess of fertility!

If you're the DM you decide (go for it!), if you're not, ask the DM how he/she/whatever rules it.

Sidenotes:

1. Since the goddess Kiltzi is not in the 5e edition this question probably shouldn't be tagged with the 5e edition, because if your DM accepts she's in 5e, she could be either way the DM want or she could follow the Forgotten realms Lore, so that makes it difficult to answer the question with a satisfactory result for the community. The Default answer is ''she's not in 5e''

2. As for 5e Canon, there is no answer as pointed out by Please stop being evil

3. Sune,Faerûnian greater goddess of beauty and love. and Sheela Peryroyl are in 5e so perhaps that's there you should look for (Forgotten Realms).

4. @Dan B suggested adding Aphrodite and when I searched for her I also found Freya and Hathor.

5. More info in:Love Domain

   There are three deities whom after the Spellplague lay claim to the love domain. One of them was Sheela Peryroyl (...) Sune, was the second deity whom called to her followers to find and collect beauty in all forms and things. Love must be shown daily. Many nobles in cities followed the teachings of lady firehair who thrived on her followers love(...)And lastly there was Kiltzi the Maztican goddess of love, lust, and fertility. (...)

6. This Question can give you more info:How common is homosexuality in the Forgotten Realms?

#I believe the answer is Yes if the DM accepts the Forgotten realms Lore about Kiltzi in 5e
Otherwise nothing can be said about it.

As for canon Sune, Sheela Peryroyl, Freya, Aphrodite and Hathor are probably goddesses you should check.

The Forgotten Realms Wiki is the source of my deduction (1991) but there is no other info for 5e according to Please stop being evil so that would be the DM's call:

If the DM accepts the old info here is my interpretation:

Kiltzi was the Maztican goddess of love, both romantic and lustful, fertility, and health.

As Niv Mizzet points out in his answer she is the goddess of love (both romantic and lustful) and the gender of the people in love should not matter.

So for that part I would say yes.

(...)her favored form of devotion was performed privately between a man and a woman.

Favored means she prefers love between a man and a woman, not that it is exclusive as far as I understood. It makes perfect sense that she prefers it to be between a man and a woman because she's also the goddess of fertility!

If you're the DM you decide (go for it!), if you're not, ask the DM how he/she/whatever rules it.

Sidenotes:

1. Since the goddess Kiltzi is not in the 5e edition this question probably shouldn't be tagged with the 5e edition, because if your DM accepts she's in 5e, she could be either way the DM want or she could follow the Forgotten realms Lore, so that makes it difficult to answer the question with a satisfactory result for the community. The Default answer is ''she's not in 5e''

2. As for 5e Canon, there is no answer as pointed out by Please stop being evil

3. Sune,Faerûnian greater goddess of beauty and love. and Sheela Peryroyl are in 5e so perhaps that's there you should look for (Forgotten Realms).

4. @Dan B suggested adding Aphrodite and when I searched for her I also found Freya and Hathor.

5. More info in:Love Domain

   There are three deities whom after the Spellplague lay claim to the love domain. One of them was Sheela Peryroyl (...) Sune, was the second deity whom called to her followers to find and collect beauty in all forms and things. Love must be shown daily. Many nobles in cities followed the teachings of lady firehair who thrived on her followers love(...)And lastly there was Kiltzi the Maztican goddess of love, lust, and fertility. (...)

6. This Question can give you more info:How common is homosexuality in the Forgotten Realms?

#I believe the answer is Yes if the DM accepts the Forgotten realms Lore about Kiltzi in 5e
Otherwise nothing can be said about it.

As for canon Sune, Sheela Peryroyl, Freya, Aphrodite and Hathor are probably goddesses you should check.

The Forgotten Realms Wiki is the source of my deduction (1991) but there is no other info for 5e according to Please stop being evil so that would be the DM's call:

If the DM accepts the old info here is my interpretation of how it should be handled now in 5e:

Kiltzi was the Maztican goddess of love, both romantic and lustful, fertility, and health.

As Niv Mizzet points out in his answer she is the goddess of love (both romantic and lustful) and the gender of the people in love should not matter.

ET got home's answer does a fine job at suggesting how to handle it in 5e.

So for that part I would say yes.

(...)her favored form of devotion was performed privately between a man and a woman.

Favored means she prefers love between a man and a woman, not that it is exclusive as far as I understood. It makes perfect sense that she prefers it to be between a man and a woman because she's also the goddess of fertility!

If you're the DM you decide (go for it!), if you're not, ask the DM how he/she/whatever rules it.

Sidenotes:

1. Since the goddess Kiltzi is not in the 5e edition this question probably shouldn't be tagged with the 5e edition, because if your DM accepts she's in 5e, she could be either way the DM want or she could follow the Forgotten realms Lore, so that makes it difficult to answer the question with a satisfactory result for the community. The Default answer is ''she's not in 5e''

2. As for 5e Canon, there is no answer as pointed out by Please stop being evil

3. Sune,Faerûnian greater goddess of beauty and love. and Sheela Peryroyl are in 5e so perhaps that's there you should look for (Forgotten Realms).

4. @Dan B suggested adding Aphrodite and when I searched for her I also found Freya and Hathor.

5. More info in:Love Domain

   There are three deities whom after the Spellplague lay claim to the love domain. One of them was Sheela Peryroyl (...) Sune, was the second deity whom called to her followers to find and collect beauty in all forms and things. Love must be shown daily. Many nobles in cities followed the teachings of lady firehair who thrived on her followers love(...)And lastly there was Kiltzi the Maztican goddess of love, lust, and fertility. (...)

6. This Question can give you more info:How common is homosexuality in the Forgotten Realms?

#I believe the answer is Yes if the DM accepts the Forgotten realms Lore about Kiltzi in 5e
Otherwise nothing can be said about it.

As for canon Sune, Sheela Peryroyl, Freya, Aphrodite and Hathor are probably goddesses you should check.

The Forgotten Realms Wiki is the source of my deduction (1991) but there is no other info for 5e according to Please stop being evil so that would be the DM's call:

If the DM accepts the old info here is my interpretation:

Kiltzi was the Maztican goddess of love, both romantic and lustful, fertility, and health.

As Niv Mizzet points out in his answer she is the goddess of love (both romantic and lustful) and the gender of the people in love should not matter.

So for that part I would say yes.

(...)her favored form of devotion was performed privately between a man and a woman.

Favored means she prefers love between a man and a woman, not that it is exclusive as far as I understood. It makes perfect sense that she prefers it to be between a man and a woman because she's also the goddess of fertility!

If you're the DM you decide (go for it!), if you're not, ask the DM how he/she/whatever rules it.

Sidenotes:

1. Since the goddess Kiltzi is not in the 5e edition this question probably shouldn't be tagged with the 5e edition, because if your DM accepts she's in 5e, she could be either way the DM want or she could follow the Forgotten realms Lore, so that makes it difficult to answer the question with a satisfactory result for the community. The Default answer is ''she's not in 5e''

2. As for 5e Canon, there is no answer as pointed out by Please stop being evil

3. Sune,Faerûnian greater goddess of beauty and love. and Sheela Peryroyl are in 5e so perhaps that's there you should look for (Forgotten Realms).

4. @Dan B suggested adding Aphrodite and when I searched for her I also found Freya and Hathor.

5. More info in:Love Domain

   There are three deities whom after the Spellplague lay claim to the love domain. One of them was Sheela Peryroyl (...) Sune, was the second deity whom called to her followers to find and collect beauty in all forms and things. Love must be shown daily. Many nobles in cities followed the teachings of lady firehair who thrived on her followers love(...)And lastly there was Kiltzi the Maztican goddess of love, lust, and fertility. (...)

6. This Question can give you more info:How common is homosexuality in the Forgotten Realms?

#I believe the answer is Yes if the DM accepts the Forgotten realms Lore about Kiltzi in 5e
Otherwise nothing can be said about it.

As for canon Sune, Sheela Peryroyl, Freya, Aphrodite and Hathor are probably goddesses you should check.

The Forgotten Realms Wiki is the source of my deduction (1991) but there is no other info for 5e according to Please stop being evil so that would be the DM's call:

If the DM accepts the old info here is my interpretation:

Kiltzi was the Maztican goddess of love, both romantic and lustful, fertility, and health.

As Niv Mizzet points out in his answer she is the goddess of love (both romantic and lustful) and the gender of the people in love should not matter.

So for that part I would say yes.

(...)her favored form of devotion was performed privately between a man and a woman.

Favored means she prefers love between a man and a woman, not that it is exclusive as far as I understood. It makes perfect sense that she prefers it to be between a man and a woman because she's also the goddess of fertility!

If you're the DM you decide (go for it!), if you're not, ask the DM how he/she/whatever rules it.

Sidenotes:

1. Since the goddess Kiltzi is not in the 5e edition this question probably shouldn't be tagged with the 5e edition, because if your DM accepts she's in 5e, she could be either way the DM want or she could follow the Forgotten realms Lore, so that makes it difficult to answer the question with a satisfactory result for the community. The Default answer is ''she's not in 5e''

2. As for 5e Canon, there is no answer as pointed out by Please stop being evil

3. Sune,Faerûnian greater goddess of beauty and love. and Sheela Peryroyl are in 5e so perhaps that's there you should look for (Forgotten Realms).

4. @Dan B suggested adding Aphrodite and when I searched for her I also found Freya and Hathor.

5. More info in:Love Domain

   There are three deities whom after the Spellplague lay claim to the love domain. One of them was Sheela Peryroyl (...) Sune, was the second deity whom called to her followers to find and collect beauty in all forms and things. Love must be shown daily. Many nobles in cities followed the teachings of lady firehair who thrived on her followers love(...)And lastly there was Kiltzi the Maztican goddess of love, lust, and fertility. (...)

6. This Question can give you more info:How common is homosexuality in the Forgotten Realms?