Federal case law protects the rights of people to refuse service based on protecting business interests. LegalZoom has a nice blog post on it [0]. Unruh Civil Rights Law does prevent arbitrary discrimination though.
If you owned a retail store, and someone came in every day yelling and screaming and breaking things, would you say they should have the right to do so, since the store is open to the public?
Why? If you really feel strongly that this is practical and everything should be allowed, you can go ahead and offer your own Nazis-and-pedophiles-welcome streaming service. I don't see why others should have their freedom of association revoked just because of your personal whims.