Squirrel Girl’s description specifically mentions her having mutant powers, but she’s lacking the affiliation so she doesn’t trigger Apocalypse’s stun immunity.
Squirrel Girl’s powers are from a mutation, but not specifically from the X-gene mutation. So while she she may be a mutant, she is not a Mutant (with a capital M), which is what Apocalypse cares about.
Edit: I believe the technical in-universe term for her is “mutate”
Is Spiderman a Mutant?
“With MUTANT powers”
First 3 words of her bio IN GAME.
Admittedly, I have no knowledge of Squirrel Girl in the comics, so if she was bitten by a radioactive squirrel then cool, I learned something new!