Ultimately, there's one reason why Leonard Bernstein transformed from a front-page musical sensation to the subject of an 800-page FBI dossier: McCarthyism, aka the "Red Scare." The Red Scare was a truly bizarre and terrifying chapter of United States history roughly sandwiched between the end of World War II (1945) and the onset of the space race between the U.S. and USSR (1955), although History says things lingered until the late '50s.
Right when the U.S. was propping itself up into a position of global, military-enforced dominance, it came to head-to-head with a rival that it needed to demonize through all propagandistic measures possible: the Soviet Union. This period overlapped with other politically-motivated, communism-abutting U.S. incursions into foreign soil in the form of the Korean War (1950 to 1953) and the Vietnam War (1954 to 1975). And so it was that "communism" became the new "Hitlerism," as another FBI memo wrote of Bernstein in 1952, per The New Yorker. The U.S. government — spurred on by the "shrieking denunciations and fear-mongering" of Senator Joe McCarthy of Wisconsin," per the University of Virginia's Miller Center — tracked and persecuted its own citizens and brought anyone considered an internal threat to the country's stability under the proverbial knife.
So it was that the FBI tracked Leonard Bernstein for decades. Even as late as 1970 Bernstein, a Jew of Ukrainian heritage, was suspected of every calumnious buzzword under the sun, including expressing "anti-Zionist and pro-Arab statements," as The New Yorker shows.