As other fellow commentards have already pointed out, a better education with special emphasis in critical thinking and a healthy degree of distrust of media sources and social media would get rid of most of these issues.
I think you'll find that a very large selection of the population, and I would guess a sizeable majority don't trust any media sources much (or government). However, rather than this being due to devious manipulation on Facebook by the FSB, it is years of hard, dishonest work by British politicians, civil servants, papers, the BBC, and commercial broadcasters that have achieved this. Consider the coverage of Hillsborough, Saville, Gulf War WMD, the Cliff Richard raid, the fake Sheikh, phone hacking, and many, many others. Its interesting to note that social media did not play any part in those various news scandals, even the most recent ones. But hey, let's focus on Facebook! I'd agree Zuck is almost as dislikeable as Bashir Assad, and that the FB business model is exploitative. But how's Zuck different to that ghastly old turd who owned the News of the World, and still dominates published media? I'd fully expect Turdoch to be lobbying for more regulation of social media.
It's very easy to point to the ample cruft, lies, and distortions on social media and tabloid web sites, and complain that the peasants are being misled (usually it seems because the peasants don't agree on some unrelated issue with the person complaining). This seems to be driven by ideas that there exists a vast class of peasants, a lower life form, unable to judge anything for themselves, and who if properly educated would agree with views of their self-judged betters, busy looking down on them.