//She can refuse though, just don't give the reason, just say you're fully booked.//
Need to be a bit careful with that. It the photographer declined the booking saying she was already booked and somebody then made a subsequent enquiry (for a mixed sex wedding) and was accepted, the circus begins. The days are gone when a trader can decline to accept business without reason when people with “protected status” are involved.
In the Belfast gay cake case the Supreme Court ruled in the baker’s favour on the basis that it was the message requested on the cake (“Support Gay Marriage”) rather than the sexuality of the person requesting it. The baker contended that he would refuse to make such a cake for anybody, regardless of their sexual orientation. They held that under the European Convention on Human Rights (ECHR) no-one could be forced to promote a belief or opinion they did not believe in or profoundly disagreed with.
The case took over four years to reach what everybody thought would be its conclusion and The Northern Ireland Commission for Equality spent £250,000 of taxpayers’ money on its involvement. However It looks like a bit more of taxpayers’ hard-earned dosh will find its way into the pockets of M’Learned Friends because In August 2019 Gareth Lee, the plaintiff in the case, instructed his lawyers to challenge the Supreme Court's ruling at the European Court of Human Rights. The UK's Human Rights Act, of course, was designed to mirror the ECHR and remove the need for people to go there for decisions on the Convention. That seemed to work well.