Well, that's not precise. They are simply objecting. Others are listening to them. I have a right to tell you to go eat a pile of dung[0], for instance. Should you then go eat the dung, it is not that I exercised my right to make you eat dung.
They are simply participating in the once-maligned "cancel culture" which was protected as "freedom of speech is not freedom from consequences". These kinds of escape hatches always have these results because one's enemies find a way to use them as well.
0: Just for the sake of argument. I'm not actually insulting you.