How would one categorize or label police officers who participate in "shakedowns?"
Morally, there is only way to categorize police officers who participate in "shakedowns," or extortionate activities. They are, in a word, "corrupt." Legally, officers engaged in shakedowns are violating laws against extorting money from individuals or groups engaged in legal and illegal activities.
Police corruption, not only in the United States but in all countries, is a problem as old as the profession of law enforcement. One of the most prominent cases of police corruption, which included shakedowns, involved the New York City Policy Department's Special Investigations Unit (SIU) during the 1960s and 1970s. During that period, detectives assigned to SIU routinely extorted money from drug dealers and other criminals in exchange for forgoing arrests or for destroying evidence used in criminal investigations.
There have been many other instances over the years of police officers shaking down suspects, including the 2001 case of Chicago police officers found guilty of attempting to extort money from undercover federal agents posing as civilians, the practice of Texas law enforcement officers shaking down citizens during the 2000s, and the 2004 case of Neward, New Jersey, police officers extorting money from drug dealers prostitutes. And that's just in the United States. In much of the developing world, police corruption involving extortion and bribe-taking is endemic. The below link to a study on police corruption in Afghanistan is a notable case in point.
In conclusion, then, police who participate in shakedowns are categorized as criminals.