Freedom from religion

[Neo-Scholastic]

And what if it has nothing to do with LBGT issues? Must a parochial school rent its auditorium for a divorce party?

If the parochial school rents to the general public, makes no stipulations in their rental advertisements/agreements and does not inquire as to the nature of the party, then yes. 

There is this thingy called "due diligence". Due diligence needs to be applied in the face of their convictions.

Edit: If the school/church has a history of rentals to entities that do not hold their convictions, the school/church has opened the door and forfeited their right to say no.

There is difference between renting to a celebration/organization that takes no express position contrary to the churches beliefs (like a chess club) and ones that do, like a divorce party, craft beer fair (for temperance denominations), or bingo fundraiser (for those opposed to gambling).

I'm very suspicious of the notion that the government can force people to do things they don't want to do for the privilege of being allowed to do the things they want to in the absence of a compelling state interest. It presumes that individual rights are granted by the state to be given and taken away at its discretion.