That's a very naive take.
Older children and adults can tell that fantasy isn't real, yes, but they can also tell the difference between the fantasy narrative and the real world setting in which the fantasy happens. Of course a propagandist can tell their "this is how the world is/should morally be" story as part of the real world elements within a fantasy story.
Kids and teen stories have done this forever after all - give kids heroes that exhibit the character and behaviour adults want those kids to emulate, give them a setting where society acts like we wish it did with values we want them to believe in not like it actually does.
Any story with a strong moral heart, which Dr Who clearly is, with its immortal god-in-a-blue-box hero saving the day against various threats, is a perfect place to embed character/value building messages through the simple mechanism of having the hero exhibit whatever value or quality you want to promote.
I have been wondering whether Propaganda is a better fit than grooming, or indeed if there is even a difference.
Then I thought about what grooming - not the consensual "grooming the next CEO" type but the malevolent "grooming someone to act in my interests believing they act in their own" is, and I think at heart it is teaching someone that what you want from them is something they want to give you, either because "everyone does it" or because "they are special".
So there's probably a spectrum between propaganda and social grooming, but looking at the two ends, the propagandist says "this is how the world should be, and these are your enemies who are trying to stop it", and the groomer says "this is how the world is, if you want to be normal/special/morally good you need to align with it, ignore those other people who want you to think differently"
I think RTD's Genderist proselytising probably sits somewhere in the middle.
All that said, and even though I think he's being a manipulative toad, the "transRose can solve this problem that neither Donna nor Doctor can because (s)he is beyond the binary..." did fold his propaganda into a nice plot.