It's generally legal to curse at and insult police officers. But the issue has been litigated in courts — and there are some exceptions to the rule.
Washington state's Supreme Court last week threw out an obstruction-of-justice case involving a minor who insulted police officers — calling them "motherfuckers" — as they detained his sister, the Seattle Times's Jennifer Sullivan reported. The state court concluded that the juvenile was within his First Amendment rights when he cursed at the cops. The court noted that while the boy's "words may have been disrespectful, discourteous, and annoying, they are nonetheless constitutionally protected."
So what is the legal standard for insulting and cursing at cops? The Marshall Project's Ken Armstrong explained:
The court's finding reaffirmed a principle with a long and geographically sweeping history in the United States, to wit: People are allowed to call the police names, even really bad names, and really, it's hard to imagine a name much worse than "motherfucker." (Editor's note: Just because you can, doesn't mean you should.)
There are exceptions to this, of course. But in general — as the examples below attest — as long as people don't resort to conduct that threatens violence, or use "fighting words" likely to incite a violent response, they can go ahead and tell police what they think of them, be it through profanity, gesture, or donut reference.
Armstrong walked through several examples of cases at state and federal courts involving words like "asshole" and "czar" and gestures like the middle finger. In each case, courts sided with the person disparaging the cops as long as the insult didn't threaten violence or wasn't inherently likely to incite violence in a reasonable person.
People should, of course, be respectful to each other and not throw unnecessary insults and demeaning gestures at police officers. But if they do break the Golden Rule, courts have decided that cops shouldn't arrest them for it.