Not invalidating the person’s rights. But corporations don’t have the same rights.
Example:
Corporation refuses to hire black people and blasts racist remarks across their web site. Illegal. Fines. Shut it down.
The CEO of that company refuses to shop at a black-owned store and blasts racist remarks across a personal blog web site that has nothing to do with his corp. Asshole. Might get his ass beat. Might make people not want to buy his company’s products. But not illegal.