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You can. That’s the point.

The headline is wrong and this is a free speech case, not a religious case, specifically the question of "whether applying a public-accommodation law to compel an artist to speak or stay silent violates the free speech clause of the First Amendment."

The idea is that the government can't compel someone to endorse a particular message. This includes the commission of creative works that someone disagrees with. This is NOT a general right to refuse service based on protected characteristics.

So you can't make a Jewish baker bake holocaust cakes if they don't want to (yes, this is an actual example that came up). But if someone is already selling holocaust cakes, they have to sell them to everyone regardless of race or sexuality.

I believe that "not religious" is considered a religious belief. I'm pretty sure that "religious" beliefs can even include things like not wanting to take a vaccine (according to some courts).