Lets say a migrant population does in fact have some "dangerous idea" that the locals don't want.

How big does that migrant population need to be before they have a sizable enough voting majority? Do the couple thousand people who moved from SF to Oregon or Seattle really really have the voting numbers to sway politics that much?

It's the idea that's contagious, not the people. Disenfranchising transplants does not stop the idea. If you want to stop the idea, you need to offer something better (or prove why the idea is dangerous).