Private people, groups, companies though? Not only may they curtail speech more or less arbitrarily in places they own, I believe quite firmly that they may respond to the exercise of freedom of speech by exercising their freedom of association and refraining from further commerce with the speaker because of the information the speaker has revealed. And with very few, narrow, specific cut-outs, American law agrees with that premise.
"freedom of association" is what a lot of people who owned diners felt enabled them to deny services to black people. Maybe you still feel that they should have been able to refuse service to anyone for any reason including skin color. We collectively decided that society works a lot better when we infringed on the rights of diner owners in order to protect the rights of everyone who wanted a seat at the lunch counter.
There's an argument to be made that in exchange for the privilege of corporate personhood, any company offering services to the general public should be required to serve any member of that public no matter what their beliefs. I'm not yet convinced that's an ideal situation personally, but situations like this make me more sympathetic to the idea.
I'd rather see our government take steps to make sure that no company is allowed to be in a position to oppress the American people leaving them without recourse. I'd sooner see companies with monopoly power broken up or pathways cleared to bring in meaningful competition. That should help protect the American people from oppression by non-governmental agencies while preserving the rights of companies to discriminate according to ideology (if that's a value we think is worth protecting).
We notably did not and that is a key distinction. We carved out very narrow obligation upon business owners to refrain from refusing service in a very specific set of intrinsic categories that have no bearing on the content of one's character. At the federal level, we notably stopped short of things like political affiliation.
In most states you can be refuse service for being a Nazi. Hell, a police officer was recently refused service because the obligation he has to open carry a firearm on duty ran afoul of the establishment's "no firearms on premises" policy (https://www.insider.com/san-francisco-bakery-reems-refuses-p...). The key difference is intrinsic versus malleable properties; a cop can go off duty and put the gun down, a Nazi can stop advocating for the genocide of people, and a KFer can cease to associate with a site tied directly to organizing abuse.
You can make a case that promoting the common welfare is served by maximizing the corporate obligation to serve citizens, but if you're trying to make it the burden's on you to explain why it promotes the common welfare for a person to serve those they know wish for their genocide or actively organize hate mobs against them.
... Anyway, I'd love to continue this thread, but as this site owner exercises their right to filter the content on their own site, I'm limited to the number of responses I may give per period of time. And that is reasonable, it is their site. ;)
We have a very narrow carve out of service obligation that constrains businesses from refusing service for intrinsic properties. Apart from that, at the federal level: no, we don't and shouldn't obligate businesses to serve Communists. We don't obligate them to serve Nazis. We don't obligate them to serve the KKK. We don't obligate them to serve Democrats. A business that's too picky about the color of people's money is a business that leaves money on the table, and that is almost always counterweight enough.
https://news.ycombinator.com/item?id=37316078
But as demonstrated by it being flagged, in practice it's too often code for "I don't like this, so NOBODY should be able to see or reply to it".