Can I refuse to speak to my former best friend?
But why would you ever want to shut them out?
I don't think they think of me as relevant anymore.
I'm sorry that is how you are feeling. It is expected that good friends will still talk to each other. You shouldn't assume they are feeling a certain way or not, just give it a try and see.
Eh, I don't care that much. I'm just going to refuse to talk to him.
You will regret it, if you want space to think you should at least speak to them and let them know that you won't be able to talk for a while. It would better than to ghost them.