I have no dispute on restaurant, motel, hospital, and other public establishments, but wedding photographer and cake designer are artists. What about goldsmiths, painters of portraits, and software developers? Can you be compelled to work? What about priests then? This is the slope that fuels the money.
Once again, I know the history of restaurants and public establishments you down voters[1]. You are wrong about a restaurant since they can be compelled (as it should be since they are a public establishment and licensing takes care of that). We already have a case of forced labor in a photographer which is why the churches are worried about being compelled to perform by the state.
1) don't ever think that it didn't happen to others
They can be offered the choice, "Do it, or suffer the legal ramifications.", but if they choose "suffer the legal ramifications" standard legal ramifications are the extent of what happens. You can't actually legally force them to do the work, they can choose to not do the work and accept the consequences instead.
"Accepting the consequences" is a nice way to say the law makes it illegal and you will be punished. So, yes, you can be compelled to do work. In the case of a hospital or restaurant that is a public place and licensed as such, this is a very good thing. Forcing artists (which the ruling acknowledges get no exceptions) is another and leads to the reason why churches and others will spend the money campaigning (see my original post).
I think it is important to understand the law before posting foolishness and twisting the meaning of words.