>Yep, and the answer is that there's a difference between who someone is, and someone's behavior. I can refuse to do business with a company that does something I consider reprehensible; that's not the same as refusing to do business with someone because of their sex or religion or race (or, in my view, sexual orientation). For example, I would not work for a tobacco company; I think what they do is nearly criminal.
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Were you the proverbial pizza shop owner should you be allowed to refuse to provide pizza for the executive briefings of that tobacco company?
Or to a meeting of the local skinheads?

If you claim that right for yourself, it is inconsistent for you to deny that right to people who believe that homosexual behavior is equally reprehensible.

It doesn't matter if you think they are right or not. It doesn't matter if I think they are right or not. By claiming the right to act on my/your own moral beliefs I/you must conceed the right to others to act on their own moral beliefs. Failure to do so makes you/me the despot and bigot.