You make excellent points. I do not envy hiring managers, that's for sure. How to combine respect for privacy and freedom of expression with protecting a company from undeserved harm? Maybe this the problem LinkedIn was trying to solve until it became a giant spam ground for annoying recruiters and influencer wannabes.
I do have good professional reasons to be on twitter and I honestly don't have much inclination to have political arguments there. If I did, I'd probably get another pseudonymous handle but even that carries some risk that it could be connected to you in some way.