So if a cop in uniform who was eating after getting off duty asked them to keep it down, could he be arrested for threatening them? Of course not.
I have three small children, and occasionally they get a little loud. As long as I am asked politely, I don't see a threat.
A cop has no right to enforce noise restrictions where none exist at a public place of business. Intimidating others under the color of authority has serious consequences. He would be most likely be terminated, and the department sued, if this had happened while in uniform.
Wrong analogy. A police officer has legal authority to enforce the "peace". Individual officers may step over the line at times, but that is a judgement call. I would think if a uniformed police officer would have entered the diner the group would have quited down on its own.