1st Amendment question regarding gay marriage

I was looking for local folk concerts and one of the nearby venues is a Friends (Quakers) church. They had a link on their front page from 1986 which stated:

Which got me thinking, there are some states which say that achurch can legally marry a couple and have that binding (with subsequent submission of application). So, if a church in one of those states decides to start marrying gays, shouldn’t they be protected under the first amendment to do so?
(I figured that this might be a GQ, but do to the nature of it…)

No.

A church official may (in many states) legally officiate without need to be independently registered with the state – that is, a Catholic priest may not need to register further with the state before he can conduct a wedding – but that doesn’t translate to carte blanche to marry couples independent of other requirements of state law. Nor should it create any First Amendment claim that the practice of the church should override state law if the two conflict, as we learn from Employment Division v. Smith, 494 U.S. 872 (1990).

A religious group can “call” anyone married they want. That does not make it legal as far as the State is concerned. The State will not recognize the same-sex marriage.

There is no First Amendment issue here that I can see.

A church can call anything it likes “marriage”, but that does not make it a legal marriage. For example, a church could say that you remain married to your deceased spouse, but if you went and married another person, it would not be bigamy as far as the state is concerned, because the state does not allow marriage with a deceased partner.

e.g. look at polygamists like some of the nuttier LDS offshoots. The State is not obliged to recognise those marriages.