The real question is whether you think a restaurant should have the right to discriminate against gays, black people, jews, swedes, poor people, poorly dressed people, etc. I think they should. It's not because I think discrimination is ok.
I see two problems here. First, you seem to be contradicting yourself. Either you believe it's OK to discriminate or you don't. If you think a restaurant should have the right to discriminate based on sexual orientation, race, religion or attire, than you believe discrimination is OK. You may not practice such discrimination yourself, but your statement makes it clear that you don't have a problem when other people do practice such discrimination.
The second issue I note is a little more subtle, but I think it too deserves attention. Specifically, discrimination based on something like attire, which is relatively easy for anyone to alter to meet a businesses' requirement, is inherently different from discrimination based on an inflexible aspect like ethnicity. In other words, I can change my shirt and tie without too much trouble, but I can't ever change the racial makeup of my parents, grandparents, etc. Conflating these two types of discrimination is, in my opinion, intellectually dishonest. It leaves people with the false impression that restrictions on 'discrimination' are simply trying to limit or curtail the ability of businesses to make *any* choices regarding their clientele, customers, policies, etc. That's not what's going on here. The question at hand is, "In Arizona, will a restaurant be able to post a sign that reads, 'We refuse to serve gays.'"