Can you give an example? I’ve never heard of such a case. You might be thinking of scenarios where people are arrested and prosecuted for resisting arrest, making threats against police officer, or crimes of that nature.
There will be limits of what you can say to police before you also run afoul of laws against public nuisance. Just as you would not want a random person to shout epithets and slurs at you and follow you down the sidewalk talking trash at you, which may be a misdemeanor crime in some jurisdictions (like disturbing the peace), the same is likely true for police if you were to interact with them in that way.
I cannot imagine anyone being prosecuted for publishing criticism about the performance/behavior of individual officers during a police encounter after the fact, or publishing criticism of the police department in their city generally.
While interacting with police, if you are being detained, beyond providing any information you are required to provide by law, which differs by state and circumstance (such as if driving a motor vehicle) - know your rights and obligations - it is wise to say “I invoke my fifth amendment right to remain silent” in response to any questions; as a suspect there are only downsides to having a conversation with police as anything you say can be used against you in court. During an interaction with police is not a wise time for criticism of police in general, the department in particular, or the specific officers at the scene.