When the definition of the group is something they have in common that makes them deserve it, then "fuck you" is a perfectly legitimate free-speech expression of anger toward that group.

Let's say, for example, that there are ten million people living in low earth orbit, and every day they dump thier shit and piss out the window, and as a result Earth's atmosphere comes to smell like shit and piss for everyone on Earth. And suppose that the LEOs know it and do it deliberately. Do you suppose the people of Earth might have a right to identify the exact behavior in question and give a hearty FUCK YOU to the LEOs who are pissing and shitting on them? It may not be "polite" to say it, but it perfectly expresses legitimate anger.

And suppose there was a group of researchers that invented a robot they call a "virtual pediatrician" that monitors a child's facial expressions, and whenever it detects a smile on the child's face, it quickly scans the environment and if it doesn't find the child's parents nearby (facial recognition previously established) it grabs the kid in its metal arms and zooms away to prevent the kid from having any further contact with whatever made them smile that wasn't their parents. And suppose some of us identify and criticize that behavior of the "virtual pediatrician" and its inventors using terms that aren't considered "polite" to use. I would call that a perfectly legitimate expression of anger, and far less offensive than the behavior that prompted it.

To anyone who thinks words are more offensive than despicable injustice, FUCK YOU.