

Silencing themselves is counter productive. They need to do the opposite. They need to use their platform to make as much noise as possible.
They can and should protest in other ways, but to sit out is to give the other side what they want, and to squander their ability to affect change.
It can create a hard place. If the current government is a rock, these late night hosts can create a hard place, to catch the network between. The network cares about money - if the government starts taking away licenses, they can’t make money, so they’ll roll over (as they have done). But they can’t make money without their talent either, so the hosts can push back from the other side to maintain their platform/voice.
Will it work? Maybe not. Will giving up? Definitely not.