I'm thinking of disallowing my son to go to church at all until he's older
Is there something he did wrong at church?
Yes, he got a little bit in a fight with a kid there when they were playing
He is your child and your duty to take care of well, and if church is a bad place for him to be in at the moment you are good for taking him out. He can learn religion and pray at home, that is no problem. You wouldn't want him to accidentally hurt more children in the church.
This isn't about that not hurting the kid, I want to take him out specifically to embarrass the family of the kid he fought with, who was his best friend.
You shouldn't embarrass the family that your kid hurt, it is not fair to them. You should consider teaching your child to apologize and maybe teach him to treat others well . Otherwise he will have a hard time making friends.