Must he prove his beliefs are “deeply held,” though? Anyone should be able to refuse service to anyone, for any reason. Specifying “deeply held religious beliefs” is problematic, IMO.
While I agree with that, the issue is the anti-discrimination laws in all states would not allow you to do that.
Thus, the problem in states where sexual orientation is listed in that law.
The other states, you can still reject working for a gay wedding. The laws are an attempt to prevent that from being an issue in those states.
But, they are ultimately too broad so far and could lead to a lot more than just giving people the right to reject baking a cake for a wedding etc. Unfortunately, they are so broadly written from the KS one to AZ, that it could even come to hurt Christians at some point since basically any religious objection can result in denying service.