It does not matter what definition you use for any gender. If we believe individuals have an individual right to privacy, then no one should be forced to share a bathroom or locker room with anyone.

Your argument seems to be that if a biological woman does not accept a fully transitioned transperson in the bathroom, then she is bigot and forfeits any rights to privacy. You never "forfeit" your individual rights, you simply don't have a right to impose your values on others.

So, a biological woman that rejects a transwoman can't force her to use a "men's bathroom", nor should you be able to force her to share a bathroom with someone else, even another biological woman.