the obvious evidence that propaganda persuades no one

 Is the Fox News watcher persuaded by what the NYTimes says? Not at all. Whatever the NYT presents only confirms the Fox watcher's beliefs about the NYT's bias. Is the NYT's reader persuaded by Fox News? Nope. Propaganda serves to confirm the beliefs that its audience already believes or wants to believe. Propaganda does not persuade. Far from it: it confirms the negative judgments about the out-group. Propaganda serves to confirm one's conviction that the out-group is morally and informationally defective and dangerous.  

Two facts emerge: propaganda doesn't persuade, and political polarization belies the post modernist and the Marxist assumption that the culture has a single discourse of power. There's no systemic belief structure directing all minds. Liberal democracy has a structure of mutually out-grouping, with the in-group significantly determined by accepting anything the out-group rejects, all the while developing and innovating means of rejecting the Other. 

In this innovation the Right has been particularly fecund. It used to be the conservatives who were stuck in the mud of the past. Now the Right is full of reinvention of natioalisms and conspiracy theories, while the Left is stuck with its Enlightenment principles and its self-righteous moral superiority and censoriousness. .