You say "using social and economic pressure to silence someone" is censorship. You're therefore claiming that pressuring a news station not to air the ideas of a certain person is the "moral equivalent of book burning."

Is it only pressuring a news station not to air the person that is censorship? If pressuring a news station not to air the person is censorship, then the news station deciding of its own volition not to air the person must be censorship as well.

All right, so a news station deciding of its own volition not to provide a platform for someone constitutes censorship. What about a person who publishes a small newsletter? Should they be required to grant column space to a person with whom they disagree? Isn't it censorship for a Catholic newspaper to refuse to publish an article on the benefits of abortion and gay marriage?

Keep in mind that you've called this sort of censorship to "the moral equivalent of book burning."

"Freedom of speech is important. Therefore, organizing economic protests should be grounds for a lawsuit." You really think that's a solution? Do people not have the right to spend their money they way they want now, or to advocate for others to spend their money they way they want?

What happened to personal liberties? Individuals and corporations don't owe any duty to broadcast messages they disagree with. News platforms might owe a duty to society to report things that are newsworthy, but there's a difference between informing the public that Alex Jones is growing in influence and giving Alex Jones an hour of softballs in which he can freely peddle his idiocy.

It's a weird day when I'm more libertarian than you.

EDIT: Also--a private corporation is not a public forum. It's not even a limited public forum. It's a private corporation which can say whatever it wants. NBC could switch to 24/7 Islamic prayers tomorrow if it wanted.