Sorry, but those outside are as much a part of the service as those in the church.
No,not really. Inside,in full view of the family, it is disruptive, and possibly hurtful.
Outside, it is a legitimate and well deserved expression of contempt for the mayor.
Outside, one is an observer of the ceremony, not a part of it. Now, at some point, e.g. as the casket is put in the hearse, the police officers could become part of the ceremony, as an honor guard or as a unified display of their respect for a fallen brother - at such a time the move would be inappropriate.
Outside, when the mayor is speaking inside, not so much.