Most of the world's population that do live in liberal democracies with free press also believes all kinds of conspiracy theories. I doubt you could find a single trustworthy source that could prove any significant difference between the two.
I'd say the US and Russian populations are just as susceptible to conspiracy theories and propaganda, but Russia's propaganda is on another level and much more blatant. Their line seems to be further than the US'.
From my experience living in Russia I would say if you _don't_ believe in conspiracy theories, somewhat in the line of all democratic regimes being fake and secretly ruled by some invisible shadow global government, you are perceived as weirdo and an outlier. That's purely anecdotal of course, I couldn't find any studies that would show the numbers.
Edward Bernays, the father of modern public relations/propaganda, wrote in the 1920s about such flaws of democracy. He directly employed terms similar to "shadow government". He was not a fringe dissident or "conspiracy theorist", he was a influential member of the establishment, who participated in the overthrow of Latin American governments. You really should read at least the intro of Propaganda (1928). Here are the first three sentences:
> The conscious and intelligent manipulation of the organized habits and opinions of the masses is an important element in democratic society. Those who manipulate this unseen mechanism of society constitute an invisible government which is the true ruling power of our country. We are governed, our minds are molded, our tastes formed, our ideas suggested, largely by men we have never heard of.
This is written by a guy who did that for a living.
Acknowledging the systemic flaws of liberal democracy is not a conspiracy theory. In fact, it is the opposite: it explains the reality of modern democracy in terms of structural factors and incentives. That said, he also describes actual conspiracies e.g. how particular advertisement campaigns operated.
This was well-understood a century ago.
The people who regurgitate what they learn in their state-approved textbooks/movies are more akin to conspiracy theorists; it requires a certain level of fantastical thinking to believe that USA (or RF), on a national level, is a de facto democracy.
There is a lot of actual conspiracies. Much more than conspiracy theories. The only known working process to uncover a conspiracy is to conduct an investigation and then prove the findings in a court.
