I understand your concern. The standard would seem that if the cause for the protest is serious the protesters should also look serious as a reflection of the cause.
The look that protesters or joiners of the protest should show is the job for the organizers. Before a protest march the organizers may orient the would-be joiners on the purpose of the protest and how they should look. This is on the side of the organizers. However, there is the side of the joiner. S/he may be new to the cause or s/he may have not fully internalized the cause so s/he feel light-hearted about it. During the march, s/he may be talking to a fellow of same level of orientation and talk of other things like the weather or a singer.
The protest march serves other purposes. One is to ventilate the cause. Another is to recruit more people into the cause. The new recruits will show varied looks in their faces or varied levels of behavior. These variations must be tolerated.
Troopers of an army on the march look very much alike, or they have timely cadence because they have been oriented many times on that behavior. Protesters are not so oriented likewise. Their commitment to the cause will soon deepen and their behavior and looks will change correspondingly as they join more protest movements. But for the first timers, joining is a good start.
If the organizer wants a serious look and very similar behavior of protesters, that can be done. It will take time and effort to attain that objective.