Not if you stay within 400 feet AGL of the mountain terrain. You can be over 400 feet MSL (mean-sea-level) but still be within 400 feet above-ground-level from where the drone's sitting in the sky.
If I'm still following the plot, this means protesters just need to get their mountains to follow ICE activity (but remain 3000 feet away, laterally) for lawful recording.
Only if you’re caught. It’s perfectly fine to put your body and life on the line and go paragliding at those altitudes but the moment you strap a headset on for FPV, it’s “illegal”.
I go out on top of the highest local mountain and send a drone up to 12,300' and the FAA won't care. I do the same thing over my house, they would very rightly be quite upset. (But I think it's BLM would care about the drone over the mountain--it's wilderness terrain, no powered vehicles of any type except for emergency use.)