A comment in the code, which I assume was the logic that Etis (Catnip's author) used to justify Androgyny requiring you to have a muzzle: "it unties face description from femininity stat, so you can use femininity to change gender aligment without having feminine face - you can't really recognize gender from animalistic muzzle!". I don't really agree with that last point, but as a non-furry, I don't think I'm best suited to judge that.
As for Flexibility, it's basically contortionism, which is something that already happens in humans IRL (and in-universe, presumably other humanoids, too) - it makes sense that it could stick around if you TF away from its prerequisites. Remember, this isn't a "blind" TF; it's entirely possible that those prerequisites are a result of its microsurgeons' programming, rather than something inherent to the perk itself.