The mature and decent and loving thing to do is to acknowledge (1) the feelings are real and (2) the feelings are not acceptable or feelings you should allow to stay.
It's in the same category as feeling jealous when a friend accomplishes something that matters to you and that you've been failing at. It's human and understandable to feel that feeling, but when we're at our best, we immediately go "whoa, that's an inappropriate and unsupportive thing for me to feel. Time to work past it."
Maybe that's where you're at and I'm making an assumption, in which case I'm sorry. But it sounds like you're suggesting that OP's feelings are valid in the sense that we should respect them and endorse the moral virtue of their existing (not true) vs. valid in the sense that they're real feelings and need to be felt/dealt with, but not valid in the sense that the emotional motivation behind the feeling is immature and a character flaw to work on (true).
It can be helpful to ask: "if I took this feeling to its natural conclusion, what would it call me to do? What is the feeling suggesting be done?" If the action the feeling would call for is something unacceptable or wrong or immoral, the feeling was wrong too.
It seems to me like the natural conclusion of "I'm anxious and self-conscious because my girlfriend is visibly trans in public" is "break up with her." Not cool. What else would be the point? Simply to be aware? For what purpose?
I think OP needs to take more responsibility for growing as a person. His GF deserves that.