You ask "How can we be sure this isn't a load of propaganda to make sure we all wear masks?" Yes, it is meant to persuade us to wear them. It is also true. The two are not either/or, they are and/and.
So what possible reason could the experts and the government have for putting out "propaganda to make sure we all wear masks"
The only sensible reason that comes to mind is that masks are going to make fewer people succumb to the virus. We then just need to decide whether that a sinister reason, which should make us instantly and automatically do the opposite?, or is it a good reason, which should convince us to wear the damn thing and get protection for ourselves and for others? The is really only one answer, isn't there?