In Yelchin's depiction of the USSR under Stalin, it's all about fitting in—or else. Anyone who does not strictly conform to the expected political purity is held suspect. That means even if you were a natural-born citizen of the Soviet Union, you're probably still only minutes away from being accused of something by somebody. Just like how quick Stukachov is to sell out Sasha's dad. But if you're an outcast in another way, you're doubly suspect in Breaking Stalin's Nose. So, people like Four-Eyes Finkelstein and Sasha's mom don't stand a chance, since they're foreign and set apart already.
The definition for "enemy of the people" seems to change throughout the book, which adds to the people's paranoia.
Even though Sasha doesn't seem to know it, he's an "other" from the very beginning of the novel.