What other word can be used to describe that behavior?

If there was one that carried the same "doesn't really care just wants to be seen saying a particular thing" connotation without triggering half the left people would instantly adopt it because there are tons of instances where you see that kind of behavior and want to call it out. Grandstanding is also close but carries the wrong connotations of wanting to influence opinions whereas "virtue singling" is toward your own tribe. Bike shedding is also close but implies actually caring about the outcome or wanting to contribute to the discussion in a non bad faith way.

There are plenty of specific phrasing that can be applicable. "Feigning outrage." "Speaking in bad faith." "Muttering meaningless shibboleths." Virtue signaling itself has become a virtue signal, an empty jargon that denotes the user as a particular tribe.