For example, let's say a member of the general population calls people with different political views irrational, and opines that they would raise the quality of some website by leaving.

Plenty of US liberals consider people who voted for Bush irrational and wouldn't want them to be part of the political discourse. The same goes in the other direction.

If that person followed through by stalking them and downvoting (manually?) all their past comments, I would conclude he had a mental illness.

Welcome to the internet. There are plenty of people who misbehave in online forums. Most online forums are simply not very public about members who they ban and whose posts they delete.

I don't think stalking is a good word for the documented behavior in this case as all actions happened on this website. There are people who actually do get stalked for things they write online and who do get real life problems from the stalking.