This cake case does specifically have to do with a CO law, but yes there's the possibility of SCOTUS ruling on some aspects of that CO law in
303 Creative LLC v. Elenis. Will be interesting to see how that one goes and the limits of the ruling since all they took up was the freedom of speech clause and not the freedom of religion clause. Or if they eventually take up Phillips's case on appeal assuming the CO SC affirms the CO appellate court decision.
It's not a coincidence we're talking about cake, food. Sustenance required to live. The Civil Rights Act of 1964 made it illegal to refuse service based just on who someone is. Their race, color, national origin, religion, or sex. Age, disability, and veteran status were added later. This means a town cannot all get together and decide they won't sell food or housing to black people and thereby effectively ban all black people from their town. No one is being forced to create, they're only being forced to provide equal service to all if they choose to provide a service.
You can throw out a platitude like that but it doesn't make it true. Some businesses, mostly in rural areas(especially in the South), would be lauded by their local populations if they refused service to transgender people. They would be more successful, not less. Your free market isn't the solution to every problem.
So your sentence contains several different issues.
1) forced: what do you mean by forced? We've mostly been talking about the Jack Phillips cake cases wherein he's never being "forced" to bake a cake. He's always free to close his shop and not sell cakes if he has a serious moral/religious conviction. I would assume the same in your artist's case. Literally forcing him to do it, at gunpoint or whatever, is wrong obviously.
2) paint: So this is an interesting case study as painting is usually subjective right? The value depends on the viewer. If you're talking about an inherently creative unique original work there's a strong argument that that's speech and hence protected. But if you're talking about painting a room in your house yellow there's also a strong argument that that's routine commercial work and not speech. Either way that's a compelled speech issue that goes directly to the freedom of speech clause in the First Amendment and would have to be litigated to find the boundaries.
3) against their closely held beliefs: You can refuse service to anyone for any reason that isn't one of the listed protected conditions. So their closely held belief would have to be discriminating against a legally protected class, which is why the cake case is so interesting as he's claiming it's his Christian right to discriminate against gay and transgender people. I agree with
the courts that both "the act of baking a pink cake with blue frosting does not constitute protected speech under the First Amendment," and "that CADA’s prohibition against discrimination based on a person’s transgender status does not violate a proprietor’s right to freely exercise or express their religion." That covers both the freedom of speech and the freedom of religion(free exercise) clauses. So they have to follow the CO state law(CADA).