Let's assume that all the issues are binary (i.e. you are either for or against a proposition). But there are a large number of them. Humans are lazy. We try to use few categories to organize people we come into contact with (e.g. left or right, colored or white).

What will happen next? We feel that "the other side" seems to be all around, almost half the population. Example: many who oppose abortion probably also believe Black Lives Matter.

Fine, but do their hair-brained ideas and failure to think critically merit shutting them out of public discourse?

They're clearly not shut out. There are major news outlets that represent them, and their voices are heard loud and clear all over the internet. One of them was elected president FFS.

If they're shut out of public discourse, why do we keep hearing about them?

They aren’t shut out. It’s not a left vs right thing. Whether your ideas are hairbrained or not, left wing or right wing — if you incite violence they should take away your account.

If they can't stop threatening people, yes.