I think the biggest misunderstanding of the first amendment and a person's right to free speech is that many people forget that it only keeps the government from punishing you, it does not protect you from criticism or punishment from your neighbor, employer, host, etc. as long as they adhere to other laws. An employer or social media host may reserve the right to fire you or kick you off their website, but the moment someone lays their hands on you, you can try them for assault. But you can't be tried for how you express yourself unless it's slander, hate speech, and so on. A good way of looking at it is "your rights end when another person's begins".

Whether I agree with it or not, Twitter is within their rights to do as they please with their platform. The ability to post through Twitter's services is a privilege.

Similar to this topic is a topic I heard on NPR. Should the president be able to block people on Twitter? Is it a form of censorship to shut down people's voices and ability to be heard?