Isn't that the definition of censorship? I'm surprised they don't actually use that word in the lawsuit: http://www.washingtonpost.com/r/2010-2019/WashingtonPost/201...
Given the countless flawed or flat-out wrong positions the Supreme Court has taken over the centuries when it comes to individual rights, I think we can likely agree they are not always right in their conclusions.
They weren't trying to constitutionally base it. Does that help?
Twitter's best line of argument is to go directly to violation of their First Amendment rights, and avoid getting side-tracked on questions of "is this censorship" and "is censorship constitutional in the general case".
Not that the government gives a fuck, but still, just to be clear about what we're discussing here. But yeah, "obscenities laws" are most certainly unconstitutional.
What is "the freedom of speech?"
You can take it literally: the freedom to say anything you can speak. You probably don't want to go down that route, because the obvious corollary is: "fine, then the First Amendment doesn't cover publication, electronic communications, or expression" because those things are outside the dictionary definition of "speech."
You can also treat it as a phrase that has meaning in context, like "object" does in computer science. But you can't have your cake and eat it too: the same interpretive process the Supreme Court has used to create exceptions to the freedom of speech has also been used to take the freedom far beyond what literally qualifies as "speech." This is particularly true if you're talking about obscenities laws, which mostly deal with things like images and performances which aren't literally speech.
Really happy to see more companies doing this though!