That depends very much on the business and the situation as a whole.
For example, I wouldn't mind if some homophobic racist piece shit owner of a local bar in Arizona would deny handing me over a drink, but it would be problematic if the only ISP in town could refuse a gay person as a customer or if all gas stations in Arizona would decide not to offer their services to owners of "gay cars". and what if you're living in a small town with only one grocery store and the next town is hundreds of miles away? Perhaps you don't care because you live in a place where there are plenty of choices, but that's not always the case.
So to answer your original question: Yes, in many cases the state should regulate business and tell them they must not refuse service to gays, christians, people with freckles, or brunettes. It's kind of obvious if you give it some thought.