Correction: I fell for a folk etymology
Reader Ian M. Slater writes:

My Latin dictionaries and grammars may be out of date, or my memories of them (since they are mostly in storage after a move) may be wrong, but I was under the impression that *propaganda* is "for the extension of...," from *propago,* "to extend, to generate," by way of *propagatio.* The resemblance of the *-anda* ending to *(pa)gani* would be coincidental -- except that they are both permitted under the laws governing sound combinations in Latin.

I am not citing English dictionaries on this, since so many of them persist in repeating dubious etymologies from nineteenth-century sources (try comparing explanations for the Latin root of "person").

Also, although the explanation of *paganus* as "rustic," hence, "not part of urban Christian culture" is generally accepted, there is an alternative explanation as "from beyond the boundary," with the metaphorical implication of "not initiated." This actually fits some contexts from late antiquity much better. Of course, both etymologies may have been current then, and invoked as appropriate.

One of the frustrating problems of philology is how one separates out real etymologies of words from 'folk etymology.' I appear to have fallen prey to this problem here, since it seems like "propagatio" is more plausible.
Now, my error isn't as bad as, say, aruging that the word "therapist" is actually "the" "rapist," but its the kind of thing that drives hard-core philologists crazy. At the last meeting of The International Society of Anglo-Saxonists, one German philologist was particular ferocious to someone who suggested that the word "fulwiht" (baptism) might have meant "full" "white" (i.e., completely pure). There's a German cognate to 'fulwiht', and so the suggested folk-etymology wasn't necessary.

To give myself a little benefit of the doubt, however, I'll point out that the kind of play on words of "for" "the rustics" would be a form of paranomasia, a rhetorical device beloved of the 10th-century, Benedictine Reform writers that are my research focus. The problem with dealing with writers who use paranomasia is that you are never 100% sure when they are using the device and when you are reading too much into a word's physical form.

This is also the case in Tolkien studies, most famously with the word "Moria," which Tolkien created in one of his elvish languages ("Mor" meant 'black' or 'dark'). Some critics read a lot into a putative link between "Moria" and the biblical "Moriah." As can be seen from JRRT's letters, this psuedo-connection (as he saw it) really drove him crazy.

This is a useful point for a larger discussion or authorial intent versus cultural resonance, but I think I've already done a good job of taking the focus off of my error in the etymology of 'propaganda.'