To be completely honest, if you'd have lived in my parents house, you'd have already been beaten to a pulp for even mentioning a wig or anything that was considered non-Christian at all, so I say that at least your parents are being physically rational, although emotionally stupid. To be honest, your parents cannot legally "make" you or "prevent" you from doing any single tiny thing that isn't against the law, and they also legally cannot kick you out, stop feeding you, stop buying you clothes, physically hit you, or take anything away from you that you bought with your own money. However, they can stop you from hanging out with friends by refusing to drive you to social events, and if you drive with your own gas money, they can stop you from going to social events if they involve the police.
I say that you should act and dress gender neutral at your house (no crazy wigs, no pink outfits, it's not hard to put up with neutral feelings for awhile) and simply be yourself when you're out with friends or at school. Carry clothing items with you, or wear items that are gender neutral but hold a great importance to you emotionally. Also, if your school has a dress code that prevents you from wearing certain items, your parents do not want you to get in trouble over that when it comes to school life. But yeah, I say always carry a backpack full of your preferred items, and change when you can; it's what I had to do.
Elsewise, continue to talk to your therapist, ask her to say something about your parents irrational emotions, and if your therapist supports your parents instead, quit going to her before she harms you and your family relations by making your parents feel "right".