I don’t see why not. There are some churches which forbid interracial relationships.
Similarly, churches can and pretty regularly do discriminate on the basis of gender. For example women can’t be Orthodox Rabbis, Catholic Priests or Cantors and women can’t sit with men during prayers at Orthodox Synagogues and most Mosques. Also, both Muslims(with some exceptions) and Orthodox Jews don’t allow women to sit with men during prayer services.
<apropos of nothing> I initially read that as “forward our evil atheist gods!” and was momentarily bewildered. </aon> 
Catholic priests do not marry two people during a wedding (and I seriously should make a macro for this), they witness marriages which are performed by the spouses-to-be. Some Catholic denominations or rites have married priests, but those priests and their spouses married each other, they were not married by the other priest who witnessed the ceremony.
An RCC priest may perform and witness a wedding where neither partner is RCC.
If one spouse is RCC and the other one is not, the one which is not is asked to accept having his children be baptised and receive instruction in Catholicism - which is not the same as “be Catholic”. Note that the officially-Catholic spouse is not explicitly required to have the kids baptised or to instruct them in Catholicism, as in theory they’re saying they want to by declaring themselves Catholic.
The Catholic spouse must promise to do all in his or her power to raise any children Catholic. The non-Catholic spouse must know of this promise, but makes no commitment of his or her own.
Perhaps the fear arises from a slippery-slope sort of perception. The public is aware of things like a facility that hosts wedding receptions being sued for refusing to allow same-sex marriage receptions. The public sees headlines like “Church sued over gay marriage,” but does not take the time to read the article and discover that the suit was from a woman furious that her church’s pastors had allowed a same-sex “commitment ceremony” and sought the return of years of tithes.
I think that a church that rents out its facilities to the public for things like wedding receptions is not being unrealistic if they believe they may someday be told to either host a same-sex reception or be sued. But that’s a different concern than the one the language quoted by the OP addresses.
Even without any additional legislation, I believe current First Amendment law would protect any clergy from being forced to solemnize a same-sex marriage.
This is true. Misinformation can run rampant. Before gay marriage became legal here, I had an argument with a co-worker over it (I know, I know, bad idea), in which he claimed that a church in B.C. had been forced to disband because it refused to recognize a gay couple. This of course didn’t make any sense, and I found that what actually happened was that the priest (it was an Anglican church, if that matters) had decided to bless a same-sex couple, and had its charter removed by the next level up of church authority (which was their right, but dickish).
Presumably they need all the help they can get, what with the not existing and all.
Or perhaps they’re just in serious denial.
“Aren’t you Mars, God of War?”
“No, you’ve got the wrong guy! I’m just Mars the gardener. You must have misheard.”
The freedoms in the first amendment are not absolute. We just found out that freedom of religion does not extend to refusing to pay for contraceptives. Why is it irrational for someone to think that the freedom to not marry someone for any of the civil rights issues might eventually be trumped by their right to get married? I mean, there are already people today who think that a business should be required to service everyone, crying discrimination (video) when an antigay congressperson is not served in a restaurant.
And, note, I have no problem with SSM. In fact, my hope is that the various churches give up their anti-gay stances, because I can’t see a loving God allowing someone to feel exclusive attraction to other men, and then forbidding it like it was some sort of wrong choice. Either the text is being misinterpreted, or God is not the God they think he is.
That was about religious groups and health insurance coverage for their employees. Nobody was arguing that churches had to give condoms to people coming in off the street, and you don’t have to work for a church to get married in that church. I think religious groups will gradually change their position on this issue over the decades or they’ll get left behind, but they’re not going to have to change because somebody sues them. They’ve always had the ability to turn down whoever they want for whatever reason they want.