Oooooh, interesting.
The complaint states that "the work of apprehending and arresting individuals has been the sole and exclusive province of members of the bargaining unit," and that the city did not inform or negotiate with the union that the chief would be "performing bargaining unit work."
Because of this, the union says the city violated the state Labor Relations Act and the Policemen and Firemen Collective Bargaining Act.
"We're not out to bust his chops," Sgt. Bob Martin, police union president, said. "It's not against the chief. The action is against the city."
Srellim, what gets them riled is not the fact that he was non-union, it's that he's the boss.
Police Union Members = Widget Factory Employees
Police Chief = Supervisor
Would a union be in the wrong to file a grievance with the NLRB when a supervisor, in violation of the collective bargaining agreement (read: "contract"), starts working on the assembly line? That's what happened here.
The Police Chief can't be protected by the NLRA, though I'm sure the Police in general aren't, but are probably operating on a public union law modeled similarly. Supervisors are exempt because Congress didn't wanting them to have mixed allegiances. It's not like he's opted out of membership, it's that the job he performs makes him ineligible because, effectively, he represents the City.
Is it better? Maybe, maybe not. The police are special because they're public servants out meant to support public safety. But it's a different issue than what you wrote. This is a contract dispute.