What is the word that describes people who are easily influenced by propaganda or always do what all other people are seen to be doing without much thinking?
I know of no word quite so specific, but gullible describes anyone who is easily fooled.
Conformist / conforming - has the strong connotation of someone who "goes along" but not of that being a bad thing. One might (rightly) conform to a law one doesn't happen to like, or (wrongly) conform to a mob's violence or social injustice.
Suggestible - someone who takes on thoughts and ideas from others without conscious consideration
Susceptible (to propaganda) - can be influenced/affected
Influenceable (by propaganda) - as above
Malleable - bendable, implies resistance on some level that is ultimately suspended. The analogy is to metalworking.
Compliant - someone who complies over-readily
Sheepish - used in a certain sense, it means someone who follows a herd mentality. It can also mean shy or cowardly.
Lemming - (noun) means someone who follows a crowd even suicidally