Americans are so enamored of equality that they would rather be equal in slavery than unequal in freedom.
Alexis de Tocqueville
If a baker doesn't want to make a type of cake, if a singer doesn't want to sing a particular song, if a photographer doesn't want to photograph a type of event, that's fine. And no one is insisting that this should be any other way. However that business can't pick and choose, providing the exact same service to one person, but refusing to provide that service to another.
For example, a baker that makes a penis shaped cake for a bachelorette party can't refuse to make that same cake for a gay persons birthday. But if you went to a second baker and asked for penis shaped cake which they had never made for anyone, then they'd be 100% within their rights to refuse to make it.