Um, no. Claiming this violates the "First Amendment" means you don't understand the constitution. The idea of "free speech" encompasses more than just government censorship. The terrorist attack on Charlie Hebdo to silence them is a free speech issue, for example.
As Wikipedia puts it: "Freedom of speech is a principle that supports the freedom of an individual or a community to articulate their opinions and ideas without fear of retaliation, censorship, or sanction." 
In turn, "censorship" includes "private institutions" like corporations. QED: Twitter censorship is indeed a "free speech" issue. It's just not a "First Amendment" issue, and indeed, government preventing Twitter from censoring Alex Jones would itself violate the First Amendment.
Libertarians like myself simultaneously oppose Twitter censoring political content like Alex Jones AND the idea that governments would forbid such censorship by a private organization. Just because we pressure Twitter to stop political censorship doesn't mean we want new laws.
We've never had private institutions of the scale of Facebook, Twitter, YouTube, and Apple that now regularly exceed the government in their power to shape discourse around the world. Insisting their censorship doesn't matter because they aren't governments is stupid and wrong.
