It seems pretty obvious the most basic way to see through the bullshit is to listen to both side's propaganda as a starting point to analysis of reality.

It's almost like the First Amendment was a good idea.

I know several people that grew up behind the Iron Curtain and they all listened to Western Propaganda (in secret) on a regular basis for obvious reasons. All of them grew up listening (in secret) to Led Zeppelin, Pink Floyd, etc.