We definitely prefer to do business with organizations and firms that reflect our social and economic beliefs. It's not a must though. We occasionally shop at Whole Foods and I'm pretty sure the owner of that chain does not agree with us on a lot of political issues.
In this particular case tho, we would never have eaten at CLA so they won't miss us. Factory farmed meat/mass production crap food is, IMHO, a far more deadly and immediate threat for the US than anything these guys could say about gay marriage. The anti-gay thing is ridiculous, 3rd century thinking, but the tide on that has turned and the days of the bigots will pass. In the meantime, food from places like CLA is literally killing us and is doing terrible damage to the environment. If there should be any outrage, I think it should be at that.