the only reason its odd to me, is because it's under your clothing. what you wear under your clothing, should be choice.
there are plenty of reasons a none trans person would bind, for example, large breasts get in the way. maybe the binder helps with back issues, this that, etc.
i'm just saying that i understand their house, their rules, but it's also your body, and your hidden body for that matter.
it's not like when 15 year olds get piercings and their parents yell. but it's an undergarment that may be very important to you physically/mentally etc.
i say you go to the therapist, but you pick one out. even if they don't specialize in gid,, you pick out someone youre comfortable with and you do what you have to.
stand up for yourself, but obviously with respect to your family. i always told my mom, "i know it's gotta be really hard for you to accept these changes, because even i am accepting myself and changing. this is not just MY transition. we all are going to transition in different ways together."
good luck. you're in my thoughts friend<3