> And as a matter of principle, they should not. When in uniform, a police officer is not a private person, who has rights, but rather a representative of the government, which does not have rights, but authority delegated to it by the people.

Oh, they still have rights when in uniform. Eg at the most basic, the right not to be killed. But you are right about the free speech. Just like any other employee in their capacity as an employee, only more so.