In my primary education, early 80's era, we learned all about propaganda. I remember those few days very well as they were eye opening!
We studied the 7 basic forms in the context of advertising. Everyone found samples of each, and created an ad centered on a favorite of the forms. Once that made sense, there was some additional discussion on propaganda aimed at citizens, with samples and discussion.
My own kids, did not get this, and a lot of other basic and important civics related education. Of course, I did it, and did it the same basic way I experienced the topic, and the results were similar.
The First Amendment does not contain a shield. This means a few things many Americans are struggling with right now, and I believe that struggling centers on the lack of civics education and a cultivation of victim culture related to news / media / opinion consumption / discussion.
The answer to free speech we don't like is more free speech!
Let them put propaganda here. When we educate our people, and our press is functional (right now it's not very functional, being largely access journalism), propaganda won't be all that effective. Never is.
Ask yourself, why did we quit basic education on these things?