Perhaps someone as big as Rush could have moved a giant corporation and employer to slightly modify a company policy. But certainly not somebody who just started six months ago.
He's not talking about a slight modification. He calls the mandate itself illegal and immoral.
You don't pee in your own pool. That's what he's doing. That's why he's off the air.
Strategically you don't fight with your employer on the air. And you don't start a fight that you can't win.