Private organizations should be able to make whatever rules they like which apply only on their privately financed property.
For example, I don't permit loaded weapons or rednecks in my house. My house, my money, my rules.
Churches don't qualify as privately financed since they get taxpayer benefits by being untaxed. They take taxpayer funded stuff for free, so they are required to admit all races, sexes, creeds and colors.
The only church which I have been in in the last 50 years is the UU. They welcome old, young, believers, atheists, whites, blacks, straights, gays, and anyone else who seeks spiritual enlightenment.
I've only been once, mind you, but I may go some more. They understand the rules.
The Bible-thumping Xtians don't.