PRYAMUKHINO, Russia—If there is a natural place to bring anarchists to order, it’s around a crumbling mansion here, which is where Sergei Kornilov tries to do it every summer.

It is the historical family home of Mikhail Bakunin, the father of modern anarchism, who was born here in 1814 and whom Mr. Kornilov describes as “our inspiration, a candle for what could be a better life.”

Each...