Hot take: Let the press document things, and leave the burner-phone stuff to security professionals. The press more or less requires attribution, so let them front that risk. Meanwhile digital anonymity starts at point-of-sale and is not easy for just anyone to pull off. The overwhelming majority of people are just better off just showing up "naked".

Then don't take a phone. If you're an organizer who needs to communicate, get a wifi/bt only tablet, look up mesh networks that use bluetooth and wifi, learn encryption and learn code words.

It's trivial to jam any wireless network. All jamming is it to flood the rf range with loud static. But you can still take measures to keep from being spied on.

Edit: also look into if MAC address spoofing. Not entirely sure which models of phones support that, officially or otherwise though.