Just look at all the government rules private schools must accept if they take government money.
So I’ll assume you are serious.
Regarding private schools and government money: government cannot legitimately violate the BOR (now including the 2nd amendment). This applies even to schools which receive government money. Don’t Catholic Universities get government grants, and without giving up their religion? Aren’t government searches on private school grounds still restricted by the 4th amendment? (to the extent that the 4th amendment still exists for the rest of us, anyway). Can’t presses operated by religious schools still print whatever they want?
IAMAL, but, while there may be strings attached to government funds, those strings generally don’t involve violation of fundamental civil rights (now including the 2nd amendment).