Yes, we do have such a question, and it survived closure twice. The trouble I see with that is one can easily make 1,000 such such questions "Is this statement of X propaganda", just by searching the news with Trump and propaganda...
"Trump's fearsome propaganda" mentioned in a WaPo article
Or nearly everything that Trump says (kentucky.com):
When do simple lies become propaganda? Most experts define propaganda as a pattern of intentional lies used to promote a political cause. Political propaganda influences and alters the perception of a population to create an alternative reality.
Propaganda is what a senior adviser to President Donald Trump calls “alternative facts,” to which she claims the president is entitled.
For the first time in my 66 years, I’m concerned that America is awash in a wave of propaganda. And, sadly the origin is the president himself. He is the modern-day version of Tokyo Rose and Axis Sally.
Sen. Ted Cruz, R-Texas, said Trump “lies practically every word that comes out of his mouth. And he had a pattern that I think is straight out of a psychology textbook. His response is to accuse everybody else of lying.”
(In case this is the first you've heard of "alternative facts", there's a Wikipedia page on that notion/expression.)
And that's hardly a recent theme in the press, e.g. 2016 article:
Trump [...] is a practitioner of something else again: authoritarian propaganda. This is a form of communication in which a leader concocts a fiction that offers a narrative explaining why the problems that trouble whole groups of people have a simple origin and an even simpler solution. The explanation of the problems is inevitably that some other group or groups in conspiracy with a corrupt elite are responsible for them. The solution is even simpler—namely to elect the author of the fiction as the new leader who will eliminate the elites and the other groups, thus solving the problems. The constant repetition of the fiction is a key to getting it accepted.
Or even the academic works, e.g. paper arguing that Trump is engaging in "antiprofessional propaganda".
Undoubtedly, antiprofessionalism is not Trump’s only appeal—racism, sexism, and transphobia have drawn many to him as well—but this article will focus on the antiprofessionalism in Trump’s propaganda.
Or undergraduate thesis titled "Trump and his Tweets: Presidential Propaganda". Etc.
If someone were to spam such "is this propaganda" questions for everything that Trump said and has been fack-checked as false by the media... That would get us a lot of such "Trump bashing" questions. Even if restrict that to things that are recurring themes, so e.g. that they got "bottomless pinocchios" (a special category invented by WaPo for stuff Trump says a lot and which they fact-check as false) that is still potentially a lot of "is this propaganda" questions.
These kinds of "is this propaganda" questions probably aren't as controversial as "is Trump fascist" (note the New Yorker link/juxtaposition and also the "authoritarian propaganda" quote), but one could easily make lots and lots of them, for no clear benefit except as "Trump bashing".
So should we have/allow such questions here of the form "is this statement of X propaganda"?
(N.B. maybe a "canonical question" asking something about Trump's "alternative facts" and propaganda might be a suitable "generic dupe", but I'm not sure such a question can be written in a way that would not received the same mod treatment as the ones about Trump and fascism or Trump and racism.)