The first amendment doesn't apply to my employer as I work for a private company, so you are right there. But is that true for cops who work for the government? I'm honestly not sure.
When you are on the job for the government, you are acting as a government representative and not a private person. You can be fired for what you say while on the job.
However, the police unions would never allow such a thing.
First of all, we aren't even talking about the police saying anything out loud. We're talking about them turning their backs on the mayor while at a funeral which, while not verbal speech, is clearly a form of expression that would fall under the 1st amendment.
Second, I suspect that a majority of the officers in question were not on the job while attending that funeral.
The first amendment does apply to your employer in that he can't muzzle you, or have you beaten up from speaking out. The worst your employer can do is fire you, which happens often, and that's fine.
In fact my employer can muzzle me. I've signed various documents over the years that prevent my from speaking about my employer (or past employers) in various ways.
And the fact that my employer can't have me beaten up has nothing to do with the 1st amendment. That would be assault no matter what their motivation.
The fact that your employer can't have you beaten up is because assault is illegal, not because of your first amendment rights. The first amendment protects you from being thrown in jail by the government for your speech.
