These places don't need legal protection to segregate. Many of them already do. So to a degree I see dude's point. I mean why would you want to patronize the business of a racist anyway?
Though I do see how it could be an issue for basic shyt like groceries, gas, etc. Imagine being low on gas and pulling up to a "whites only" gas station in the middle of nowhere. And I wouldn't want the govt getting lobbied to decide what are and aren't 'essential services'. So the laws make sense.
If the society you live in discriminates against a given group in every way imaginable, why wouldn't you? If you're a customer in such a society, you're likely racist yourself to some extent, so you wouldn't care about excluding certain groups from your favorite place of business. You'd likely welcome it. If by chance you aren't racist, how likely are you to inconvenience yourself to adhere to your morals? Your friends/family/neighbors/etc. likely won't think any more highly of you. If anything, you risk being ostracized for wanting to associate with the "other".
If you're a business owner, if the customers to be gained by barring that group from your business outweighs the potential customers from that same group, then, in a perverse way, it makes perfect business sense to do so.