The OP isnt about grading or names.
Example if Bob is a gay teacher and little Billy said something bad about gays(heard it from this dad), would Bob correct him because he is gay and discuss gay people with him or just correct him because speaking bad of people is wrong?
I'm glad I don't teach English, history, government, anything controversial - just stem. One student once confronted me about the garden of eden , the age of the earth - they had been home-schooled before college, didn't know how old the earth was... turned out, not a single other Christian in class - I didn't say anything... not sure the best way to handle stuff like that.
Here's another one - had a Muslim student, president of the Muslim student association, fresh out of a ... very conservative country where women wear "ninja outfits" haha, what another Muslim told me, their feminist mom refused to wear the ninja outfit ...anyway, I'm female, pregnant (huge), teaching a bunch of guys how to run these big tensile materials tests - ripping steel apart... and this poor Muslim kid is in culture shock that some lady is in there running this lab... he confronted me, a bit nasty with asking questions, demanding this and that, cold stares, I had to be on my toes, not one mistake - he was waiting for a chance to take me down, but I know my ****
.... so the last day of class he walks up with schedule. - "Is this you? Is this your class?" Hard stare, angry face. Haha, he signed up for another class with me!! We celebrated Ramadan together the next semester, that club invited me to their big feast, we sat and ate together, and they tried to explain it all to me... it's all good.