Well, let’s start off w/ the baker and the store owner. The argument is that when they open a business to provide goods/services to the general public, then any member of the general public is allowed to patronize their store/business. If the business decides not to provide the service to someone, then the potential customer files a civil complaint against the business owner. And yeah, people have won civil cases for that stuff.
But it’s not a government action.
In the case of social platforms, most (if not all) have a “Terms of Service” agreement that everyone has to agree to before being allowed to use the platform. Most of those Agreements include phrasing that says (in effect) that the owners/moderators of the platform are the sole arbiters of what does and what doesn’t fall under “Acceptable Use” under the terms of the Agreement.
Those that agree to the Terms of Service are effectively surrendering their “rights” to anything when it comes to use of that platform.
Again, if someone feels that a platform like Twitter or Facebook has violated their First Amendment rights, they’re going to run up against the Terms of Service Agreement that they “agreed” to. (Most people never read them.)
Okay, then the terms of service are as follows.
No Black, no Hispanics, and no Conservatives shall be served
at our enterprise.