How is requiring both sides to get equal air time about "silencing" anyone? If you're giving equal time to the other side, that's the exact opposition of "silencing" them.
What Republicans fear, is that if their voters hear what the other side is REALLY saying, as opposed to what the right claims they are saying, Republicans will lose voters. There are so many lies Republicans have been telling their voters about Democrats that you believe that simply aren't true.
Democrats favour "open borders" is a prime example. No they don't. Democrats reduce illegal immigration every time they're in office by prosecuting employers. Republicans refuse to go after their donors, so illegal immigration rises every time a Republican is in office and their donors put out the "Now Hiring" signs.
No one ever appears on right wing media to counter the lies of the billionaire owned right wing media which is benefitting the wealthy, and destroying the middle class. The Mercers, the St. Clairs, and the Murdochs are raking in billions in tax cuts and increased revenues, all based on demonizing Democrats and no one is calling them on their lies, or promoting an alternate view, on their platforms. And poor and unemployed white Americans aren't listening or reading any other platforms.
That's why so many Republicans believe so much that is not true.