Chicago Critical Mass currently has a fairly good relationship with the police. In the couple of years that I've been riding , the police have generally been helpful to us. Several factors play into this:
1) Tourists enjoy Chicago Critical Mass and it helps promote a good image of the city. They smile when they see a three-piece band being pulled by a bicycle. They smile when they see bicyclists on 19th century high-riders or modern day novelty bikes. They laugh when they see bicyclists wearing silly costumes. They take lots of pictures and have stories to tell their friends. They enjoy the festive party atmosphere which leaves a much better image of Chicago than the tail pipes exhaust from SUV's.
2) A street on which a Critical Mass ride is taking place is safer and has less accidents on it than an automobile-clogged road. Statistically a lot of people die every year getting run over by automobiles, whereas it's statistically rare to die in a collision with a bicycle. And the Massers aren't distracted by cell phones or by the claustophobia of being stuck insider a car -- so they are paying more attention to what they are doing than they typical motorist.
3) The Loop is maxed out in terms of how many cars that it can handle. Studies by the City of Chicago now suggest that Loop real estate is too valuable to keep building more parking garages. So being helpful towards events that get people enthused about alternative forms of transportation is considered valuable for the future of the Loop.