BRUSSELS—Power politics between Russia and the rest of Europe are once again raising a question that dogged strategists throughout the Cold War: Where is the line between prudence and paranoia?

Russia, which for years has used its vast supply of natural gas as a political lever with energy-hungry Europe, is building a nuclear power plant in Moscow-friendly Belarus. Neighboring Lithuania and Poland are so determined to escape Russia’s clutch that they refused to buy electricity from the plant.

Still,...