Various libertarians have assured me that private businesses, like private individuals, have a right to not do business with people they don't like for whatever reason.
Well,
William Blackstone, the 18th-century person who codified English common law,
begs to disagree. Money quote:
[I]f an inn-keeper, or other victualler, hangs out a sign and opens his house for travelers, it is an implied engagement to entertain all persons who travel that way; and upon this universal assumpsit an action on the case will lie against him for damages, if he without good reason refuses to admit a traveler.
You see, Jim Crow and "private association" was a radical idea imposed after the fall of slavery.