As for HAMILTON.....I think those songs are very specific to a small group of shows....In NYC,I think it's a bad idea unless you are auditioning for HAMILTON...and even then a song in "the style of" is probably a better choioce..a if you are not a person of color....probably a poor choice...Yes I KNOW that the characters they are portraying were not people of color in history but HAMILTON is a very specific musical animal.
For many years I sang WHAT DID I HAVE? I have also sung BROADWAY BABY, I have never been afraid to sing a gender bending song because I am comfortable in my public personna....so it never was a gender statement....the material was always the statement.
Then there is the question of the CD's knowledge of some material. Not every casting director is a walking encylopedia of Musical Theatre canon.
I once had to explain "who" Patty Duke was........I was reduced to explaining she was Sean Astin's MOTHER!.....today even that would probably be responded to w/the sound of crickets!