The first amendment is not unlimited. Public accommodation laws were passed because many people felt that whites and blacks shouldn't mix, and in particular shouldn't marry. This was justified based on religion. You may say that the justification was bogus, but courts don't do exegesis.
Public accommodation laws say that whatever your religion may say about different races and their mixing, you can't refuse to serve people equally. I think this actually is a limitation of religion, but the US felt that people who run public businesses can't limit service, even if it's based on their religion. This doesn't, of course, limit their beliefs, but it does limit some some categories of actions based on those beliefs.
The current debate on LGBT issues is in the context of laws passed because of other types of discrimination, but in the original context it did limit ways in which a people engaged in certain businesses act, even if it's based on their religion. So the religious impact of LGBT questions isn't new; it's almost inherent in public accommodations laws.
As far as I can tell, the Supreme Court hasn't looked at all possible limits on there laws. I think most people agree that it's OK for the law to require you to sell things to anyone, even if they're KKK members. Where it gets murkier is services. But we probably also want to require hotels to accept everyone, and that can involve some services.
While not all possible cases have been resolved by the Supreme Court, I think it's pretty clear that you can't compel someone to express a view they disagree with. The most obvious recent case is making tee shirts with messages. Do you have to make any message the customer wants? That's murky, because you can argue that no reasonable person would take the writing no the tee shirt as representing the store's personal views. As far as I can tell, this particular case (Hands On Originals) won't get to the US Supreme Court. I think the same arguments would apply to making custom cakes with messages on them, but (1) the court failed to deal with the real issue of that case in making its ruling, and (2) the baker stopped the discussion with his prospective customer before the design of the cake was relevant. So as far as I know, these kinds of questions are currerntly unclear.
How about catering? I can see that someone might not want to cater a KKK event. But we might end up requiring it, because there are too many groups that are unpopular in some area of the country.
All of these things can in fact limit actions that in some cases might be based on religious views. Invoking religion doesn't give people unlimited freedom.
Personally I'd be willing to narrow the scope of public accommodation laws slightly, not covering things with messages. I'm not so sure about catering.