In a Capitalist society, bakers are not "participating" in a gay wedding if they bake a cake for it. If they give the cake away for free, you could argue that they're participating. Since they are getting paid, it's a simple transaction, complete upon payment. The same would hold true for a catering company even though they would be forced to work at the reception.
The 1st Amendment doesn't give you the right to discriminate in a business transaction on the grounds of race, gender, sexual preference or a host of other things. The key here is the fact that it's a business transaction. They certainly can't force you to bake a cake for free.
Do you consider yourself a Capitalist Mr. Censorship?
"Can a law force a Muslim business owner to eat pork?"
That isn't the same thing. "Can a law force a Muslim caterer to serve pork?" fits the situation better. And the answer is NO, so long as his business doesn't serve pork to anyone else. The law can't make you bake a cake for a gay wedding if your company doesn't bake cakes.
"Can a law force a Catholic business owner to pay for a customer's abortion?" Again, not the same thing. For a proper comparison, your question would have to be "Can a law force a Catholic business owner to perform an abortion for a paying customer?" and the answer is NO, so long as the business owner doesn't perform abortions for anyone else. The law will not force us to be in a business we don't want to be in.
Your situation is different from both of your examples and both of mine. You bake cakes and want to refuse service to a particular person based on sexual preference. Right now, you might get away with it. The Supreme Court recently considered two cases, DOMA and California Prop 8. Had they ruled that homosexuality constitutes a "suspect classification" for 14 Amendment purposes, the Arizona law would not stand up to a challenge, but they didn't include that in their decisions.
The Arizona law is so blatant, the Supreme Court will have to hear a case, almost right away and they'll have to take the 14th Amendment into consideration this time. We all know they way the winds are blowing with regards to homosexuality. What decision do you think they'll reach?
Governor Brewer would do well to be on the right side of history, don't you think?