What's really scary about Ivan, the Gentile village mayor, is that he manages to be both a reasonable neighbor and a violent, destructive thug. When he comes to rough up Tevye's house, and Tevye is like, whoa, man, isn't this a little messed up, Ivan responds "seriously":
"We have been arguing over whether we should beat you up or not. Since everywhere else people are getting beaten up, why should we let you get away without it? So the village council has decided we should beat you up. […] We have nothing against you, Tevel […] But one thing has nothing to do with the other. We must beat you up." (9.18-21)
This is... chilling. It's logic, but of course it's completely illogical. Ivan has that only-following-orders, bureaucratic, Terminator quality of terror—perfectly friendly, but also perfectly cruel.
And of course Ivan is also a stand-in for all the people who profited from the forced resettlement of Jews when he buys Tevye's house at a discounted price. Basically, he's a symbol of everything that's wrong with the government-sanctioned anti-Semitism that's forcing Tevye and his neighbors out of the homes. You almost feel sorry for the guy.