I believe it will be difficult to provide a concrete answer to this question, as the discussions of sexuality appear to be avoided by TSR and WotC, possibly in order not to alienate young audiences. Even in a setting like Al-Qadim (that is geographically located on the south of the continent of Faerun), where concepts of honor and marriage are discussed in detail (chapters 2 & 3 in the Land of Fate), this topic appears to have been glossed over. Hence the GM is given more than usual amount of flexibility on how they reconstruct their own campaigns.
If we try to make educated guesses about the personal choices of the creators of the Realms setting, of people such as Ed Greenwood or influential authors like Bob Salvatore, it is probably safe to assume that most Realms societies have a more "open-minded" view of intimacy between consenting adults than medieval societies of Earth. For example, it is worth noting that a fair number of famous Realms characters such as Drizzt, Wulfgar, Catti-Brie, Elminster, a number of the Seven Sisters, etc. are unmarried and the novels imply intimacy shared by these individuals; although we do not read the public's reactions to such relationships.
As another example, you can read Ed Greenwood's opinions about sexual attitudes in a Candlekeep post from 28 Nov 2012 (quoted also from a second source in the answer by @Mindwin). He mentions the role of polytheistic religion as an effect that encourages clergy to "avoid endorsing discrimination against someone because of sex". He also describes that rituals for powers like Loviatar, Sharess, Sune and Shiallia can and do involve intimate conduct. In particular, he points out that as expected from her portfolio, "Shiallia wants all creatures to reproduce and multiply". But it is worth underlining that these discussions come with a disclaimer that is most often not presented this explicitly in Greenwood's other answers to Realms-related questions:
The beauty of fantasy roleplaying, and the Realms, is that anyone playing in it can include or leave out or ignore or gloss over what they want to or are most comfortable with. The darkness creeps in when one player or group tries to impose their preferences on everyone else.
Additional and arguably more on-topic answers to this question can be found in the archives of Candlekeep forums. In another post from April 13, 2004, Ed Greenwood describes dusk-to-dawn marriages, which are meant to prevent commoner females from later demanding compensation from noble males in return for their "lost maidenhead", or commoner males from claiming that they are now part of the families of the noble females with whom they have had intimate relations. Greenwood mentions:
..., the clergy of Siamorphe, representing a deity catering to the nobility, are concerned both with being popular/useful to nobles, AND safeguarding the rights, privileges, and powers of nobles. Bastard children, loss of virginity, and so-called "immoral" behaviour are matters far more important to noble families than to the general populace.
He continues with the following additional arguments:
... neither I nor the nigh-immortal [not everyone, notice, just the Chosen and other live-for-many-centuries folks, and nobles and royalty who consider themselves 'above' laws and social rules, or to be the people who set such laws and rules] fictional Realms characters I've created view "sleeping with" people as being incompatible with having deep, committed relationships with someone else.
... "swinging" between committed or married couples isn't seen as Bad by a lot of Faerunians, in many places and situations (though among most citizens across the Realms, it would be). [It's fashionable among some noble classes and a LOT of "wannabe noble" rich, rising merchants, and frowned upon in places with small, stable populations where warfare or monster predations haven't forced folk into desperate survival measures (telescoping survivors down into a single extended family of multiple husbands and wives, for example).]
This post again ends with a number of disclaimers about how Ed Greenwood feels he is treading somewhat dangerous waters.