I'm not the person you're replying to but one thing I've seen pointed out [1] is that it portrays a largely unelected whitehouse staff where everyone is selfless, good, hard-working, quick-witted, reveres the constitution, always ultimately putting the country's interests before their own, always taking the moral choice and turning out to be right.
There's nothing that makes you question the way the country is run, or that tries to explain why real-world politicians' approval ratings are so low.
Also the endless monologues where the speaker is just so correct that no one can dare question what they are saying and the target of the monologue is left speechless with just how wrong they were.
Same thing happened with The Newsroom, it's a Sorkin trademark. Although the heavy-handedness was relaxed with season two.
As far as I can tell, "West Wing" clearly is aligned with the worldview of Aaron Sorkin, just as "24" seems pretty aligned with the worldview of Joel Surnow.
I'm not sure at what point a strong worldview from a creator crosses over to the "propaganda" definition? So many shows over time have had creators with very distinctive, often strong, worldviews and opinions. I can say that about so many shows ranging from "Twilight Zone" to "Star Trek" to "MASH" to "South Park". I'm not sure I'd call any one of these "propaganda".
For whatever reason, I tend to think of "propaganda" as persuasion coming more from group collectives, such as governments.
I'd say it is coming from a group collective, because Joel Surnow and Aaron Sorkin are nothing without a platform for their shows. It's the conglomerates that own US television networks that chose to fund and broadcast the strong worldview of these writers.
Same with "The Wire". I enjoy it however I feel like it grants a false sense that law enforcement follows all the rules for obtaining warrants for surveillance.
Spoiler alert, but I recall the police figuring out how to get around the requirements of getting a warrant to be a huge plot. Perhaps it showed a rosier than normal view of police getting warrants, but I feel like it definitely displayed a variety of situations where law enforcement did not follow the rules.