I've had this issue, not with binding, but just general clothing. I'd wear skirts or dresses and suddenly people stopped respecting my gender. They said I should just "stay a girl. it's easier". I hate that expressing any femme quality just suddenly invalidates your trans identity if you're non-binary or trans masculine.

It's not like breasts or clothing is inherently female. Hell there are cis men with breasts. I wish people would stop assigning gender to body parts and clothes

TL;DR
I know that feeling. Even days where I shouldn't be, I bind because my gender is ignored or questioned if I dont. It sucks. :/