I think the reality is that they have to be seen to be doing something. Most countries have run out of ideas, they know that lockdowns are devastating for businesses so they develop this obsession with mask wearing because it's a really visible sign that you're doing something, even though masks are of very limited if no help at all. And like in DR, just keep extending the curfew because again it's a very clear sign that you're doing something.
There are a few simple and effective ways to slow down the spread of covid that citizens can follow.
This cooperation will avoid shut downs and further slowing of economies and loss of incomes.
Avoid gathering in large groups.
Wear a mask in group situations, you may include eye glasses or shades.
Wash your hands.
Not very complicated procedures.
COVID 19 is a viral infection looking for a host.
It does not care about protests or denials of its existence.