I'd argue I have a way bigger legitimate interest in keeping conservatives out my workplace compared to this photographer's interest in refusing clients. We employ many LGBT people, and have had a handful of issues where regressive assholes cannot handle working with such people and cause problems.
I can demonstrate not only direct financial impacts of hiring Republicans, but a whole host of less tangible impacts of allowing such conflict into the workplace. It's actually striking how inevitable it is.
The moment a person comes out as a Republican, it's basically a ticking clock until they will make their hate everyone's problem. As it stands we have to be extremely careful about firing these folks because of the conservative outrage machine, so if we could just be direct about not employing them that would honestly save me a lot of time.
Finally, unlike one's sexuality or gender, nobody is born conservative. If somebody reads a platform of hate and chooses to identify with that platform, then I should have a choice to marginalize such people to protect my family and business.