Likely absent because, while indifference can mean you don’t discriminate, it can also sound like you don’t care about the issues that affect gender and sexual minorities.
True, thus the "...I'll support you...". Not being bothered doesn't mean not caring about their rights and well being.
Did you ever watch The Invention of Lying? In it the main character tells his best friend and the bartender all sorts of untrue statements about themselves and the guys, especially the bartender, was so happy and supportive about everything. That's my goal. You be you, and I'll support you as long as you aren't hurting others.