[TheDong]

If you go into a supermarket and start spewing hate-speech, yes they have every right to ban you.

If you make other customers uncomfortable, they have every right to expel you.

Alex Jones is spewing hate-speech on twitter, making other twitter users feel unwelcome, and so on.

I don't see how this analogy is favorable to him at all. If you're abusive in a space to the point of causing mental pain to others, yes, you should be removed from it.