Law enforcement entities often research groups they deem subversive or adversarial. Research can involve infiltration, and disingenuous rabble-rousing ("agents provocateur"). Overly zealous approaches can cause harm, and are sometimes explicitly illegal.
The FBI ran a program, COINTELPRO, starting in the 1950s surveilling groups like the Communist Party, the Black Panthers, the Nation of Islam, and the KKK. The program, which for instance sent an anonymous letter to Dr. Martin Luther King attempting to persuade him to commit suicide, was exposed in 1971. Wikipedia 
In the 1970s-80s the Portland Police Bureau surveilled and infiltrated a number of "adversarial" organizations, including a food coop and a bicycle repair collective, as well as individuals who went on to become moderate political leaders. In 2002 an expose revealed the contents of the files, as well as the fact that a retiring police officer stole the physical files after the state outlawed the practice, and continued building the files in his own garage. Portland Tribune's "Secret Watchers" series
In 2020 there are numerous concerns about infiltration into the movement for racial justice following the killing of George Floyd. The publicized destruction of a store in Minneapolis was revealed to have been perpetrated by a police officer. (Removing a note, which seems to be contested, about a specific alleged infiltration in Portland. Twitter )