The fact that private stores can do what they want does not mean that they should do what they want or that consumers shouldn't demand otherwise. More generally, not all bad behavior is or should be illegal. The fact that the first amendment only legally applies to the government does not mean that free speech as a concept doesn't have moral force on other organizations.
For instance, we expect universities to act as neutral debate platforms for all sorts of views that are not endorsed by the university administration. When they fail to do this, they are not legally penalized (modulo constraints from accepting government funding), but we (should) lower their public esteem. Newspapers and online media companies like Apple and Facebook could and should be held to a similar standard by the public, although in practice they are unfortunately given more latitude.
For instance, we expect universities to act as neutral debate platforms for all sorts of views that are not endorsed by the university administration. When they fail to do this, they are not legally penalized (modulo constraints from accepting government funding), but we (should) lower their public esteem. Newspapers and online media companies like Apple and Facebook could and should be held to a similar standard by the public, although in practice they are unfortunately given more latitude.