Ok, you think that churches are public places. Not having to pay taxes(some private corporations) and being paid for by taxes are two completely different things.
Point two: It's a place of public worship. So the public is welcome. We still reserve the right to turn anyone away for whatever reason we see fit. Just like any other private company. Though I have not known this to ever happen at our church.
Your point three is completely up to opinion. I think it's oppresive to force someone to accept everyone and make all kinds of changes using the money of the private company. It's one thing if the government funded all these changes. But they don't. They make the business spend all kinds of money to come up to standards that may never need to be used by anyone.
I find myself leading more towards the libertarian viewpoint on issues like this.