This example is bovine effluent. Being homosexual is not hateful to any other person.There isn't a good way out of this kind of thing. Who's rights prevail?
I personally think it is reprehensible that people get denied services because the business owner is allowed to claim that the request by the LGBT individual(s) would violate religious beliefs. I think it's a poorly-concealed act of hate masquerading as a religious issue.
HOWEVER . . .
Turn the situation around . . .
A couple who openly professes white nationalism comes into your cake shop and wants to order a cake for their wedding. They specify a hateful anti-semitic, anti-Hispanic, anti-African-American message in icing on the cake advocating denial of citizenship, and worse for everyone not a white national. They wear swastikas, openly carry guns and try to leave printed propaganda in your shop and shout slogans outside.
You refuse to accept their order citing violation of your sense of ethics, civil behavior to say nothing of religious and non-religious beliefs of tolerance. You refuse to help them spread their vile message in the form of their cake and its decoration.
You defend yourself claiming that any decent person would do the same and that you cannot be forced to participate in activities that violate your morals.
They sue you citing violation of their civil rights of free speech. They claim you are attempting to deny them lawful activities.
Now what?
These are two opposite extremes, but it's the direction our increasingly polarized society is heading.
Rich
Being a photographer is like being a mechanic, neither carries the implication of support to the personal POV of their clients.