Will this promiscuously share with any other reachable running instance? Does that, combined with anonymity, create a risk that an adversary could distribute misinformation directly to protesters via this app?
No, for power reasons and the way that bluetooth works you have to expressly put the app in sync mode with someone nearby, which isn't ideal but is a good start. That being said anyone can post anything so there's certainly the option for adversaries to propagate their own information.
(EDIT: rephrased as question)