Thanks everyone for the support and advice.

I don't really think they would go as far as to kick me out, however I'm also not the type of person to go against my parents requests... generally. From what I understand, whenever my mom sees me wearing my binder it bothers her; so I guess she's taking my being trans pretty hard. I think the main issue here isn't really the binder, but the fact that she won't
talk about it. I think that talking would help diffuse the situation a little bit... or maybe I'm wrong. I don't know. Until then I guess I'm just going to have to sneak out of the house whenever I want to wear my binder.
If I went against my parents wishes, I think the most that would happen is that my relationship with them would become even more strained. I'd rather not strain it anymore than I have to.
The whole moving out thing... a friend asked if I wanted to share an apartment after her current lease is over (she can't stand her current roommate). So I just need to hold out a little while longer.
For now I might try the whole rent thing like Malachite suggested, but I don't really think it'll work. Still worth a shot though.