I believe there is a basic or 'golden' rule when it comes down to rights. You are entitled to your rights up until the point where they infringe on others. Any religious rights must be weighed against other's rights to to be free from discrimination or persecution. I can't practise or exercise any religious beliefs that might cause anyone else to be denied of their rights.

If I were bus driver would it be reasonable to to deny black people access to the bus I drive because integration is against my religious beliefs? This scenario is functionally no different than a photographer discriminating against people because of their beliefs.

I can't speak for the US but in the UK it would be illegal to force someone as part of their job to do something against their beliefs (not just religious, this could apply to vegetarianism for example). The notable exception to this is when what you are being asked to do would be reasonably expected of a person in your job.

In your analogy. You can play the game of basketball you want. No one can deny you from playing or setting the rules you agree. But you can't play all the time. Sometimes you need to let someone else use the court.