I generally shy away from "political" topics but I will say this: I am a non-believer now but went to Catholic school, went to Church at least once a week, actually read the New Testament, was an altar boy for years, etc. and everything about all of those things did nothing but reinforce the fact that the Church was a good thing. Every single priest I knew was a great guy and I still associate with one on a very regular basis. Fr. Paul is an amazing guy and actually conducted my niece's baptism where I, as godfather, was supposed to pledge to "lead her in the Church" or something and Paul took me aside ahead of time and said there was an issue as he knew I would not want to say that. So we changed the wording so it would be in the spirit of the pledge but acceptable to all. Paul has come to family dinners where there have been Jews and Muslims present and they all say there own versions of essentially the same prayer and everyone respectfully participates. No big deal. IMO Religion is supposed to be about inclusion and being a good person and respecting others and not forcing others to do or believe exactly what one thinks they should. We are all "God's creation" and should be afforded mutual respect.

Now that is the way things should be IMO but legally should they be compelled? Not if they are a non-professional service as then they are just some guy who should be able to be as bigoted as they want, however odious that may be. But if one is a professional that has taken an oath of service, such as a county registrar, doctor, pharmacist, lawyer, minister, etc. then I would look at that vow to see what it says. And I doubt any of them say that you are allowed to discriminate against someone that you do not agree with.

And fun fact: in my jurisdiction anyone apparently can use the Costco pharmacy, even without a membership, as legally a pharmacist must serve any one any product that is prescribed.

I don't know if I even answered your question as I think I just started rambling.

edit: Attributed to St. Francis of Assisi: "Preach the gospel, and if necessary, use words."