It's obvious to me -- in that it trips my bullshit meter -- that posting a sign at the Circle K on the corner that says, "Sorry, no homos." is wrong - deeply wrong - but I can't make a logical argument against the business that doesn't get into businesses being dependent on roads and police and fire and other government services, and as such, the government can make rules that force you to cater to your enemies. Businesses need licenses, and depend on state services -- after that, I got nothing. Let the shitty businesses out themselves as close-minded bigots.
It's sort of a tragedy of the commons (it looks like tyranny of small decisions is a more accurate name). If you allow discrimination in "private" business, you reduce the availability of some product or service to the group that you're discriminating against. If the availability gets reduced enough, you begin to get a class of people that can't participate in the economy, or even in society at all, because there's simply no way for everyone in that group to get what they're trying to buy, even if they have the money. Obviously this is a much bigger issue when it comes to basic necessities like food and housing, but it can still cause problems for general consumer goods and services.