Earlier quoted context omitted.
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.
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.
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.