I'm not interested in the content of an argument over the language that upset empty.
However, "My best friends are X" is never some trump card against "I am X". I understand that you feel empty hasn't earned the right to ask you to change your language to make them more comfortable. But this template of "my friends / family from Oppressed Group agree with me!" is generally one to be avoided.
Have you ever read an extremely misogynistic screed written by a person who insists that they get along fine with women, because their mother was one? Ever talked to someone who insists nobody reasonable could be offended by trivializing the Holocaust because their Jewish boyfriend is kind of into Nazi/prisoner roleplay? (I have encountered both scenarios.) That is how your "trump" reads to me. Mental illness in your family is a very personal connection, but it's not the most personal connection.