I would also note that there are existing platforms that effectively make political views a protected class. It turns out they are not very popular, because most people don't want to hang around with people for whom the 14 Words are an important political view.
In practice, a platform can either have haters or the people they hate. Insisting a platform accept all the haters means you're guaranteeing the people they hate will go elsewhere. That's why Twitter has moved away from the sort of policies you favor. As an example, look at when Milo Yiannopoulos led a wave of racist abuse toward Leslie Jones. Twitter had to choose between keeping her (and a lot of her fans and people who just don't like open racism) or Yiannopoulos and his fans.
So the notion that we should override the Bill of Rights to make Twitter platform everybody is not only anti-freedom, but also won't in practice work. If somebody doesn't like Twitter's rules, they should do what you're doing: post somewhere else. There are platforms ready and waiting to take them.
What's the concept then, other than that Twitter is doing things that you don't like? That's obviously not a sufficient argument, and if antitrust law isn't the reason for legal action to be taken against them, what's the reason? The only other legal course I could imagine is significant changes to media laws (which I'm certainly not opposed to, but those seem more difficult to argue for than antitrust action), or perhaps going at it from the other side and changing the laws around how public figures must communicate with the public.