A couple of observations:

1. What might underlie this Russian perception — which I think is over the top — is something far more threatening to the Russian psyche than the idea that America is scheming and plotting to topple them.  Far worse indeed is the truth, which is that since the end of the Cold War we’ve more or less ignored them.  A lot of what Putin has done, seems to me, to be the geopolitical equivalent of a moody tweener screaming for attention from the once-idolized cool kid who nows ignores them.  Going from being one of two superpowers, where every time the Kremlin caught a cold, Washington sneezed, to a perceived backwater minor power, is bruising.
2. Having said that, from one point of view, they’re not entirely crazy.  While I think they overestimate the coherence of any “American worldview”, there is a certain evangelizing tendency in American politics.  We’ve solved it, many Americans think, and of course everyone else should reap the benefit of our leadership.  It’s cloying and positive but threatening in its own way.  And the ongoing cultural ascendancy of American media — where our action films and pop fashions rule the world — can’t help anyone feel secure.
3. It’s hard to see what to do about this.  You can’t convince someone you’re on their side by simply repeatedly telling them that.   And our actual attitude — dismissive neglect — is unlikely to generate either the evidence of a benign attitude or reciprocal respect.  The nigh-complete breakdown of the American political machine implies more neglect and drift, with sporadic and counterproductive engagement mixed with saber-rattling for domestic benefit.  It’s a bind.

Regarding: “America has a simple ideology”: how one of Russia’s top US experts tries to explain America – Vox