The propaganda is actually the people saying there are consequences for speech and it must therefore be limited. It is a trivial observation that there are consequences but that is of course not a justification to curb it. Again, the problem with "reasonable" exceptions is that someone has to define them. Free speech means the spread of ideas, it doesn't mean you are allowed to lie if you swear an oath to a judge.

But we specifically see language policing and idea suppression in supposedly scientific institutions (hot examples: climate change, gender, wars, racism, immigration, ...).