Are you saying that we shouldn’t control for a coordinated national change in murder rate when evaluating the impact a mayor’s specific policies have had on their city?

Anti-police policies are not exclusive to the NYC though. If you want to control you need to show that murders also rise in the cities that don't have the same policies. Chicago, SF, Minneapolis don't appear a sensible choice for a control group in this regard.

I’d say the blame for the consequences of pro crime ideology should be shared by all mayors that hold it.

NYC is subject to the same national economic, demographic, and cultural trends. For example, recently there has been a respiratory pandemic that affected the entire nation.