That's like saying: Alex Jones is free to grow his own food on his land as much as he pleases. This supermarket has a policy not to sell food to people who violate our terms of service regarding hate speech.
It gets murkier when they start banning classes of people or ban someone for something that puts them in a protected class, but any supermarket that banned Alex Jones for hate speech would be well within their rights.
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.