It depends on the police. In many places the police have long practiced bogus harassment and arrest of black people (and other minorities), and this wouldn't change it.

The real role of police, in those places, is effectively to suppress people whom the political class in power find to be 'undesirable', not only criminals but homeless, political protestors, minorities, etc. In those places, the 'bogus' reports on Nextdoor are business as usual.

By the way, the political class in power (e.g., middle-class whites in some places) don't always consciously think about 'suppression'. They feel uncomfortable around the homeless person and unconsciously rationalize a reason to have them removed (he could attack someone, it interferes with local businesses, it's better for him to be in a shelter, etc.).