Many of the New York police live outside the city. I don't think it is a good idea but that is the contract they were able to negotiate. But what this means is if police who turned their back on de Blasio do not live in the city then they do not pay city taxes. They are however paid from city taxes by people who do live in the city. Bill de Blasio was elected mayor by people who live in the city. He is the representative of the people who live in the city in issues small and large. That is the meaning of representative democracy. The police who turned their back turned it on the representative of the employer. They are not part of the social organization of New York City, they are hired by them and (at least in theory) can be dismissed by them. In what other jobs could individuals who are employed by an organization turn their backs on their employer in a sign of obvious disrespect and hold on to their jobs. I venture to guess there is not a one - at least if you don't get to have a gun when you do it (and even then, could any military person turn their back on Commander-in-Chief they would be dismissed?).
Why aren't these police being summarily dismissed for disrespect and insubordination?