SeeYouSpaceCowboy is a lgbtq hardcore punk/metalcore band. Their band name is a reference to the anime cowboy bebop.
Feminazgûl is a feminist black metal band that was founded by a transgender woman.
There is also a Canadian heavy metal band called Vile Creature. They are lgbtq activist couple that makes music and also part owners of a tattoo shop. I know that isn’t quite what you are looking for, but I felt like they are worth a mention.