Second, the first amendment is clearly and unambiguously intended to protect the right to free speech from governmental interference. There are myriad outlets for speech, and as long as that continues to be the case, you can't just handwave something like "corporate censorship dampens the spirit of free speech". Argue from facts, not ideology: show that it's actually happening.
Further, there is no argument for making Twitter, Google, Facebook, CloudFlare, or any other company into a public utility that wouldn't also apply to Fox News, Clear Channel, or the Drudge Report, and compel them to publish liberal views.
Alex Jones is facing backlash from these companies not because of his reprehensible politics, but because he has been inciting violence against other people and these companies, finally, are taking some responsibility for their role in that. Maybe when he finally stops trying to convince people to go after the families of Sandy Hook victims or "investigate" pizza shops, he'll be let back onto the playground to play with the other kids.