Except if the reason they are refusing them service is because they are a member of a protected class. This was a core issue of the civil rights movement.

It could be argued that forcing a business owner to provide a service they don’t want to perform is assault by the state (protected classes notwithstanding).

What if a business owner’s religion precludes then from serving a protected class or someone with a disability? Which takes precedence?

But the business owner in this case is specifically offering to provide the service (baking a cake to your requirements) already. Unless they aren't, and they just offer a number of predesigned, off-the-shelf cakes, but it doesn't sound like that's the case here.

Not according to the civil rights act of 1964. Or the americans with disabilities act of 1990.