I'm not going to ask more about my friend coming out.
Why aren't you going to ask him about it?
It's because I don't care.
It's impolite to not be there for your friend during an important event like him coming out. I think you should support them and ask if they need anything in his difficult time.
No its fine
If you guys are on good terms it is ok to move on. I doubt gay people really want to focus on coming out all the time when they have more interesting personality characteristics.