This is a common misunderstanding -- probably committed more often by Americans than non-, though, so don't feel too badly. The fact of the matter is that private corporations (and that includes publicly traded such; ahh, the vagaries of English) are pretty much free to do whatever they want with the infrastructure they own, without running afoul of the Constitutional protections regarding free speech.
That's not to say they won't suffer some well-deserved ire if they "censor" something, but the actual First Amendment reads, "Congress shall make no law ... abridging the freedom of speech..." (The elided bit in the middle of the quote is the part about religion, often called the Establishment Clause.) They're under no legal or other obligation to "not censor"; the Congress is.
That doesn't mean AT&T haven't run afoul of any of the other Safe Harbor provisions they're subject to under US law, but that's not remotely about freedom of speech. The gist there, AIUI, is that if you block one kind of content, there's an implication that you have the ability to block arbitrary kinds of content, and so you're suddenly obligated to. (Someone who knows how the various Safe Harbor provisions is encouraged to correct any misstatements in the preceding.)
EDIT: As potatolicious points out above, this isn't as black and white as all that; when government and industry climb into bed together, they tend to get their obligations and responsibilities all over one another.
That's not to say they won't suffer some well-deserved ire if they "censor" something, but the actual First Amendment reads, "Congress shall make no law ... abridging the freedom of speech..." (The elided bit in the middle of the quote is the part about religion, often called the Establishment Clause.) They're under no legal or other obligation to "not censor"; the Congress is.
That doesn't mean AT&T haven't run afoul of any of the other Safe Harbor provisions they're subject to under US law, but that's not remotely about freedom of speech. The gist there, AIUI, is that if you block one kind of content, there's an implication that you have the ability to block arbitrary kinds of content, and so you're suddenly obligated to. (Someone who knows how the various Safe Harbor provisions is encouraged to correct any misstatements in the preceding.)
EDIT: As potatolicious points out above, this isn't as black and white as all that; when government and industry climb into bed together, they tend to get their obligations and responsibilities all over one another.