It seems we should be spending less time reacting to other people's lifestyles. I wish gays would just SHUT UP about their preferences. But refusing to sell them a service? I'm a minority of one here. It's not something that the law should support.
That is until the nudist lobby gets the same political clout the homosexual lobby has. They were born that way, after all. Why should a business owner have the right to refuse their services to a nudist?
Businesses are properties, and property rights are one of the fundamental building blocks of personal liberty. Suppose you own a Christian bookstore and a group of Pentagram wearing Satanists come in to your store laughing and giggling about how they plan to desecrate a Bible. Should you be compelled to sell them one?
All sales, even an over the counter purchase of a pack of chewing gum, are contracts, and a fundamental basic of contract law is that both parties enter into it voluntarily. Once you compel one party to participate, that fundamentally undermines the whole nature of business, and as others have alluded to in this post, is really no different, philosophically speaking, than slavery.