Imagine you run a commercial photography studio. The following scenario arises:
A potential client calls; it's the 'Holy Church of God is More Colourful than a Baboon's Arse' (not a real church, just in case you were wondering). This church wants some promotional shots of the congregation. You end the call saying you will provide a quote (as normal), and then quickly google the church to get a sense of their needs. My search turns up that this church is strongly homophobic. Wetboro Baptist Church level homophobic (you can swap that out with anything comparable that you find abhorrent if gay rights ain't your thing)
I wouldn’t refuse them business. What good does that do? They can just go somewhere else. I would take their money and be happy with the fact that a church is paying a baby-eating, devil-worshiping, god-hating heathen to do something. If you really didn’t want to do it, I’d quote them an outrageous price. If that doesn’t scare them off, you can take pleasure in knowing that the money you get will go to something other than religion… perhaps you could donate the “extra” money toward a cause that the church opposes.
Just a theory but, I see starting a business as entering a contract with the community. The business is there to service some need which the community has (in this case promotional photography) and the Church of "God is more colourful than a Baboon's Arse" is a part of that community....probably has been since before the business existed. On that basis, I would ignore their anti-gay heritage and take their business (charging full price of course).
I say do whatever you feel is right at the time, so long as you aren't breaking any laws. If I was in a position to be able to, i think I might decline the job. You could probably get out of by stating a conflict of interest (I'm assuming you are atheist). In the end I wouldn't think either choice would be an unusual outcome from such a situation.
If anyone came to me specifically wanting me to do something that directly spews hate toward another, be it they are gay, black, Muslim, or purple people eaters, I would definitely refuse. In that case, I believe I would have a case because of the hateful message. The murkier part of the whole deal is if someone came to me for work that shows nothing of their true hatred, no gay-bashing language, etc., but I know that they actively spew such rhetoric, like Westboro, that would be a little more difficult to say no to legally, I think. Right now I have a zazzle store online where I sell my designs on tshirts and other items. I have some Buddhist and Hindu quotes because I like the message (none refer to a god) and of course, designs for secular humanists and atheists. I do not have anything in reference to the Christian or Muslim religions because I don't want to be associated with them. Thankfully, I don't have anyone requesting that I do that and I have the right to create, or not create, a design for someone asking for something along those lines. I would politely steer them to another zazzle store where they specialize in religious designs instead.
I don't believe in saying no just because I'm not a Christian, but I do believe in saying no if that church or individual is into blatant hate-ranting. I can't support that for anyone.