There's no legal right, unless you are a government employee (who btw routinely censor anyway, e.g. any state university with a content-based speech policy is violating the law). But there's very much a moral right and moral obligation - if you are in a position of power, as people leading the high-tech industry and prominent politicians are, you are responsible for maintaining the society that promoted you to that power in good health.
And good health of the society requires free exchange of ideas and freedom to debate this ideas without fear of being persecuted and punished. Yes, even if you're end up being wrong - in fact, freedom to be wrong (excluding, of course, recognition that you're wrong) is vital to any proper debate, since if being wrong implies one's destruction and punishment, no serious and honest debate is possible, and no serious and honest truth-seeking through free exchange of ideas is possible either. You'd either fear to express your ideas, if you're powerless, or use your power to suppress other's ideas and punish them, if you're powerful - and that would have no relation with whose ideas are better.
Only when the exchange of ideas are free, and only when ideas can participate in this competition without prior approval by powerful incumbents, any healthy democratic society is possible.
And yes, whoever in power in such society, which now includes the big tech leadership, have moral if not legal responsibility for it - a responsibility that they are not only neglecting but blatantly violating right now. Censorship by powerful monopolies is as wrong as censorship by the government, and we need to stop hiding behind this stupid idea "but it's not government, so we can ignore it".
So in the case that participants on a social platform engage in trolling, harassment, and abuse (sometimes with bots), that company should not do anything? If some people who are attempting to exchange ideas and debate in good faith, are shouted down by people hurling epithets and death threats, the platform owners should shrug their shoulders?
When people openly promote and even plan violent attacks against others big tech should just leave things be?
I think we have more than ample proof of Big Tech companies blocking people not for abuse/bots but for expressing viewpoints that the platform management deems politically unacceptable. So let's not pretend that fighting bot abuse, spam, violent threats, etc. is the same as political censorship - the platforms can do one without the other, and actually have been doing it successfully up to about 2019, when they started increasingly censor by political views. And now political bans are pretty much commonplace. Once can pretend that it's all "fighting disinformation" and "preventing violence" but nobody is buying it anymore. It's political censorship, sometimes openly partisan censorship, and nothing more.
And good health of the society requires free exchange of ideas and freedom to debate this ideas without fear of being persecuted and punished. Yes, even if you're end up being wrong - in fact, freedom to be wrong (excluding, of course, recognition that you're wrong) is vital to any proper debate, since if being wrong implies one's destruction and punishment, no serious and honest debate is possible, and no serious and honest truth-seeking through free exchange of ideas is possible either. You'd either fear to express your ideas, if you're powerless, or use your power to suppress other's ideas and punish them, if you're powerful - and that would have no relation with whose ideas are better.
Only when the exchange of ideas are free, and only when ideas can participate in this competition without prior approval by powerful incumbents, any healthy democratic society is possible.
And yes, whoever in power in such society, which now includes the big tech leadership, have moral if not legal responsibility for it - a responsibility that they are not only neglecting but blatantly violating right now. Censorship by powerful monopolies is as wrong as censorship by the government, and we need to stop hiding behind this stupid idea "but it's not government, so we can ignore it".