Currently, are Catholic priests required to perform marriages for non-Catholics? I think they are not, even though the right to not be Catholic is constitutionally protected.

But just in case, the majority did insert language making clear that this is about what the government can and can't do, not about what religions can and can't do:

Finally, it must be emphasized that religions, and those who adhere to religious doctrines, may continue to advocate with utmost, sincere conviction that, by divine precepts, same-sex marriage should not be condoned. The First Amendment ensures that religious organizations and persons are given proper protection as they seek to teach the principles that are so fulfilling and so central to their lives and faiths, and to their own deep aspirations to continue the family structure they have long revered. The same is true of those who oppose same-sex marriage for other reasons. In turn, those who believe allowing samesex marriage is proper or indeed essential, whether as a matter of religious conviction or secular belief, may engage those who disagree with their view in an open and searching debate. The Constitution, however, does not permit the State to bar same-sex couples from marriage on the same terms as accorded to couples of the opposite sex.

There's controversy at the state level over whether religious photographers, DJs, bakers, florists, and wedding planners should be forced to participate equally in all weddings regardless of their religious belief. That's going to be the next big fight.

Photographers, DJs, bakers, florists are not religious organizations, they are for profit businesses. That's the big difference. They are business that are open to the public. The church has religious requirements for some of their ceremonies (such as first communion).

They are also often sole proprietors. Like independent software developers, they may not have a public "place" of business that is distinct from their home. What they do often amounts to contracts between private individuals and not so much businesses open to the public (like a restaurant or retail shop). I don't know enough about the law to say if this falls under a different set of rules, but it would seem reasonable that it might.

No, your local Catholic priest is not required to open the church to gay wedding ceremonies, just as they are not required to perform weddings for mixed-religion couples, or divorced persons, or any of a number of other reasons why they might object. Now, your local Justice of the Peace who happens to be Catholic? That's a different story. As a government employee they cannot discriminate.

No, they won't have to. I'll speak to this from the perspective of the Catholic Church, and how they'll avoid having to perform same sex marriages.

The Catholic Church can already deny anyone a church/religious ceremony. Suppose I'm a Catholic and was married within the Church and later divorced. If I don't receive an annulment, the Church will not allow me to remarry within the Church. I can still go elsewhere, but the Church will not perform the marriage or acknowledge it as valid (a later annulment can get the Church to change its stance on this marriage).

Similarly, the Church (in the US) typically requires 6 months of marriage preparation. If you refuse to go through it, they will deny you a marriage within the Church (a friend of mine went through this last year, they were impatient and couldn't wait the extra 4 months apparently).

With regards to same-sex marriage, the Church's stance will not change (certainly not in our lifetimes), they'll continue to view same-sex relationships as sinful. Consequently they cannot, from their perspective, sanctify a marriage of that sort. This is not, fundamentally, different from the other reasons they use to deny people a Church marriage.

Edit: Regarding your second paragraph, yeah, I hear that a lot. But they're ignoring the cases where the Church already denies marriages. I already had this discussion with a coworker who happens to be a Catholic deacon this morning. It's frustrating that so many Catholics (and others) don't realize that they've already got the freedom to deny anyone access to the sacraments. I can be refused communion by a priest if he knows that I'm an (unrepentant) philanderer or drug dealer or murderer or that I've been excommunicated by a bishop. They are not obligated to perform baptisms just because someone asks if those asking aren't willing to go through the steps and agree to the things the Church requires. They won't ordain me just because I walk up to a bishop in a cathedral and ask to be ordained. A church marriage is a similar sacrament that the Church has laid out requirements for, and refusing to comply with those means you won't get married in the Church.