Okay so I thought people weren’t going to take the naively deontic argument here, which is why I skipped it. But very well.
One, as @mitigatedchaos these aren’t really about “your property,” in as much as the CEO’s making these decisions often are not the shareholders, but managers entrusted to make the shareholders money (or other complicated legal entities”. These people have a ton of leniency in those decisions, but “what speech should be expressed” is generally not in the CEO job description. Maybe they make good decisions or bad, but I have trouble seeing fundamental property rights being worked up for the managers making these decisions. If it was a vote of shareholders that would be different.
But two, more importantly, I assume I am talking with people who think the internet should be largely content neutral. People who do not want Google to stop listing supporters of Bernie Sanders. People who don’t want Twitter blocking any criticism of feminism. People who’d be afraid if TWC stopped delivering content about either the Democratic or Republican parties. Maybe you wouldn’t be sure such actions are illegal, but you sure as hell would feel they are unethical.
Most people who are comfortable with Nazi’s getting deplatformed this way are so because they believe Nazi’s (or at least their current rioting actions) are different than just another point of view.
If you think a web company should continue to host political opinions they disagree with, but not that of Nazis organizing armed rallies, which I really do think is a reasonable point of view, then why do you think that question should be up to the CEO of the company?
(Or, to avoid the hot button topic of government regulation - I can see the argument for all hosts are open to Nazis, and the argument for no hosts being open to Nazis, what’s the argument for some hosts being open to Nazis?)