First of all, there are plenty of businesses that would do exactly this. It is legal in most US states.

OK, but I don't think it's right. Here's why.

We as a society have said, employers can "discriminate" (meaning "choose") employees on some axes but not others. They can discriminate based on where you went to college, where you've worked previously, how friendly you seem to be, but not based on your gender or race. That's true even if working with a Black person or a woman would make some people uncomfortable.

The question, which I'll leave as a question, is, what's the difference between these two sets, and in which one does LGBTQ identity belong and why?