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The Tasha's Cauldron of Everything optional level 3 Wizard feature Cantrip Formulas does the following:

You have scribed a set of arcane formulas in your spellbook that you can use to formulate a cantrip in your mind. Whenever you finish a long rest and consult those formulas in your spellbook, you can replace one wizard cantrip you know with another cantrip from the wizard spell list.

If I get a wizard cantrip from another source, such as the Githyanki's innate Mage Hand cantrip, can I replace that cantrip using Cantrip Formulas?

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It's only a wizard cantrip if you learned it as a wizard

Cantrip formulas says (emphasis added):

[...] you can replace one wizard cantrip you know with another cantrip from the wizard spell list.

Knowing a spell that happens to be on the wizard spell list doesn't necessarily make it a wizard spell for you. For example, if you are a multi-class wizard/sorcerer, you could learn Fire Bolt as one of your sorcerer cantrips. If you do so, then you always use your charisma modifier when attacking with Fire Bolt, because for you it is a sorcerer spell, not a wizard spell.

In some cases, a feature will let you learn a spell and have it count as being associated with a certain class even if it isn't on the standard spell list for that class. If so, it will explicitly tell you so. For example, the a cleric's Domain Spells feature says:

If you have a domain spell that doesn’t appear on the cleric spell list, the spell is nonetheless a cleric spell for you.

The psionic spells of the gith subraces don't say anything about counting as spells of a specific class, so you can't treat them as wizard spells.

In terms of lore, your wizard cantrips are spells that you have learned through your focused study as a wizard, while your gith racial spells represent innate psionic abilities, so it makes sense that they are not interchangeable in this way.

There is no general rule for which non-class features grant class spells and which do not, nor are there special categories of spells like "racial spells" with distinct rules; there are just specific racial features that allow you to cast spells. If the feature granting a spell says the spell counts as a spell of a specific class, then it does; otherwise, it doesn't count as a spell of any class. (And if it's ambiguous, I'd recommend asking about it on this site.)

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    \$\begingroup\$ Would you cay that this also applies for High Elves? Since the cantrip they select is specifically off of the wizard spell list (rather than a spell that just happens to also be on the wizard spell list) and can use INT to cast it, that case may be less clear than the one for the Githyanki. \$\endgroup\$
    – RevanantBacon
    Jun 14, 2021 at 14:03
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    \$\begingroup\$ @RevanantBacon To be clear, I'm not saying that spells from your race never count as class spells. I'm saying that when any non-class feature grants you a spell, it doesn't count as a class spell unless it says otherwise. As for the high elf's cantrip, that seems to be a gray area. It's not clear to me whether "from the wizard spell list" is intended to quality it as an actual wizard spell. \$\endgroup\$
    – Ryan C. Thompson
    Jun 14, 2021 at 15:46
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    \$\begingroup\$ Then that should be addressed in your answer. The Githyanki were only an example of a race that grants a spell ("such as the Githyanki's innate Mage Hand cantrip"). A full answer should address all races that have such spell access. \$\endgroup\$
    – RevanantBacon
    Jun 14, 2021 at 17:33
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    \$\begingroup\$ @RevanantBacon I think my answer is complete as is. My basic claim is that a non-class feature only grants a class spell if it specifically says so. I'm not going to go through every non-class feature (or even every racial feature) that grants a spell and judge whether each of those features says it grants a class spell. \$\endgroup\$
    – Ryan C. Thompson
    Jun 14, 2021 at 18:01
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    \$\begingroup\$ Even if you don't go into detail, you should at least address that some races might have different ways that they grant spells compared to others. \$\endgroup\$
    – RevanantBacon
    Jun 14, 2021 at 18:50
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Spells learned from racial traits are not associated with your class so Cantrip Formulas cannot be used

The Sage Advice Compendium includes the following related question:

Q. If you have spell slots, can you use them to cast the 1st level spell you learn with the Magic Initiate feat?

A. Yes, but only if the class you pick for the feat is one of your classes. [...]

From this we can see that if, say, a Sorcerer took the Magic Initiate feat under Wizard and took the magic missile spell (which appears on the Sorcerer spell list), it would not count as a Sorcerer spell. This stance is directly supported in the following:

Similarly then, a cantrip learned from a racial feature does not count as a Wizard spell simply because it appears on the Wizard spell list. This stance is also supported in the highest scoring answer to the following question:

The Githyanki Psionics mage hand spell is not associated with your class, so you cannot apply any features that rely on a spell being a class spell. The Cantrip Formulas feature only works on Wizard spells and so cannot apply to the cantrips learned from racial features.

An example of a feature that does associate a spell with your class is the Divine Soul Sorcerer's Divine Magic:

[...] You learn an additional spell based on that affinity, as shown below. It is a sorcerer spell for you [...]

The Githyanki Psionics feature lacks any similar wording.

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