C-h Freese:
I personally have know problem with a "Cleric" who has issues with homosexual marriage not doing them. If he or she opens a denominational wedding chapel still no problem, that chapel having exemptions allowing doing marriages for affiliated religions, still no problem. but they had better keep track of current issues in those denominations.
Well, there's a bit of a difference there. Churches are essentially private organizations, you don't have to let in everyone. So, if you say you'll only do weddings for members, and you have clear criteria for membership, you're well within your rights to turn down anyone else.
A wedding chapel is a business, though. They might be privately owned, but if they do business with the public, then they pretty much have to accept everyone, regardless of the owner's beliefs.
For example, a restaurant at a racist golf club might turn away black people, legally, because they only serve members of the club. That same restaurant on a city corner, not so much-- if they're accepting walk ins, they really don't have the right to cry "free association".
Someone who ran a "Baptist only" wedding chapel would tread the line, so it would get very dangerous for them. It'd be even murkier if they let in affiilated denominations, because after a certain point it could be argued that this is no different than accepting walk-ins.