Funny, I seem to recall all sorts of instances where the government has forced people and businesses to cater to those that they don't want to... Hell, Title IX is based on the premise of providing equal access by protected classes.

And for reference, political party is a protected class in DC, and that could extend to other areas. Politicians aren't allowed to block people on Twitter or Facebook, it's only a matter of time before the companies themselves aren't allowed to in many conditions.

There's also the concept of a public space in private ownership to consider. There's a big difference between your living room and a restaurant or park.