"No coloreds" was in many places a law, not a business rule. The argument that many free market supporters make (myself included) is that the market would have naturally moved toward inclusiveness. Sure, some assholes will still be assholes. And thinking people would avoid those stores, diminishing their market presence until they disappeared naturally.
Laws that forced businesses to hide their racism let racism fester. Rather than allow those people to put their stupidity on display for the world to mock, we now had racists making tons of money of "those n*****rs" they hated. They're still racist, but now they are practically legally obligated to make money off of their object of hate. Is that really better in the long run?