Say I’m a photographer with a public studio. Someone comes to me, say a Mr. Vito Corelone, and wants me to take some pictures. Can I refuse because he’s Italian, or I think a Mafia Don? No.
Now suppose Mr Corelone wants me to take pictures of his next hit against Mr. Luco Brasi. He wants to document Luco “sleeping with the fishes”. Can I refuse? I damn well should be allowed to! Can you image being forced to participate in such a thing?
Then you might say, well, this is different. Murder is illegal, gay marriage isn’t. Well actually, gay marriage is NOT legal in Arizona. So it is similar.
No one is refusing Don Corleone’s rights by not agreeing to photo his hit. They would IF they refused because he was Italian.
There, NFL, is the difference.
Once gay marriage is legal your analogy doesn’t stand up. Best argue on religious grounds of the business that they should not be forced to provide that product to those customers.