But it depends what you mean by "service".

To sell someone a cake you already make - sure.

To sell someone a cake that they want customised in a way that you don't normally do: I think you have choice here. As I mentioned in another comment, if you're an artist who paints portraits in watercolour, or in monochrome, I don't think it's reasonable for someone to demand that you paint in oil or in colours. Ultimately it goes down to your own personal artistic choice, and the kind of art and product you want your brand associated with.

It's not about refusing custom to another group. It's about refusing your products to be used in a way that specifically supports the ethos or belief of that group, if you don't support that ethos or belief. No private business should be required to make a cake with a message they consider abhorrent or immoral on it.

I'm a secular atheist, for what it's worth. I should equally be allowed to refuse to make a cake with "Jesus saves" on it: though selling someone the basic cake, and letting them add the custom icing elsewhere, that's fine.