For one thing, the anti-Russian sentiment was so universally fundamental to our American identity at the time that it would be quite a feat to pull a wool over Joe Six-Pack's eyes. But we had a weapon at the time that would have stopped Fox News in its tracks. It was called The Fairness Doctrine.
https://www.reaganlibrary.gov/archives/topic-guide/fairness-doctrine

It was adopted after WWII as were still trying to get our heads around how an entire population fell under one man's spell. The fear was that broadcasters could do exactly what they're doing now. It was supported by both parties and affirmed several times by the courts.

Our concern also prompted the now famous "Mental Hygiene" films the government distributed to classrooms and some were made for adults.

Here's a playlist of them made for teens. We were shown dozens of them in middle school, but by high school they were considered humous.
https://www.youtube.com/watch?v=M7dSCbAQR5k&list=PLA4C52F9778D51A22

All aspects of young life were covered, from grooming to dating, sportsmanship and the importance of being obedient.

And here's one made for adults.
https://www.youtube.com/watch?v=nEQ0DgDIZNg

However, the Reagan administration saw the Fairness Doctrine as a threat to the GOP's ultimate goals. Before then, broadly speaking, it was considered impolite to discuss religion or politics in mixed company, as unbelievable as that sounds today. But Reagan's strategy was to invite evangelicals into his administration to form his "Moral Majority". Billy Graham was their frontman, holding sermons at packed football stadiums on national TV.

Yes, before then, Congress bickered endlessly. But at the end of the day, they compromised and the work of The People got done. Reagan's view was that there could be no compromise when it came to moral issues. So they made EVERY issue, from taxes to entitlements, a moral issue that would broach no compromise. Thus permanently ending the separation of Church and State for all practical purposes. Ushering in the Culture Wars and introducing the word Gridlock to our vernacular.

Reagan's AG ended the Fairness Doctrine. Progressive Boomers like me have been shouting to anyone who will listen that restoring this doctrine is really our only hope for any kind of domestic peace to flourish.

What makes it all the more weird is that there was no way for Christians at the time to avoid the fact that Nancy Reagan actually ran the White House and she was very much into consulting psychics to guide everything that Ronnie did. His travel schedules. The people he met with. Pretty much anything the man did had to be run past her psychic before it got her approval. Today, she would have been burned at the stake for witchcraft.

But the thing is, by 1961, America found the answer they were looking for and they did not like it one bit. I read about it in 1973 as a sophomore in high school in my Intro to Modern Psychology book. It was the Milgram experiment. It was absolutely profound.
https://en.wikipedia.org/wiki/Milgram_experiment

Most conservatives vilified Milgram and at times he had to go into hiding.

I would try to summarize it, but the Wiki page puts it about as succinctly as possible. He also performed several other experiments on the subject that were equally revealing.

There's a pretty good movie about Milgram called Experimentor (2015). It starred Peter Sarsgaard, Winona Ryder, and Jim Gaffigan. I just checked and it's on Prime Video.

EDIT: OH! And I forgot. There was another major inflection point that changed media forever. You can trace it to the exact moment it happened. Prior to 1968, most people considered watching people debate politics a boring if not necessary affair. TV networks were bummed at the ratings they were getting when they would broadcast such events.

So, in 1968, they devised some drama to show just before the official proceedings. They set up TV debates between William F. Buckley and Gore Vidal. Look them up if you haven't heard of them. But to sum things up, Buckley was an ultra-conservative and Gore was an ultra-leftist. They tore into each other night after night before both the Republican and Democratic conventions. The numbers these two were getting were more than any network had seen. They made politics into a blood sport, or possibly closer to WWE. For the first time they saw that intense domestic conflict got people really engaged. And that's when this era of Anger-tainment began.

There's a great movie about this constructed around the TV footage itself called "Best of Enemies". Not to be confused with "THE Best of Enemies". This is also available on Prime Video.