Open your wallet and donate.
There are organizations already embedded in these movements. They know what they need, they typically don't have the money to get it done.
I know it won't satisfy that itch to find an engineering solution, but your $$ are truly are the best way to support.
I think you should look here for some ideas of how the future will pan out if these conditions continue, it might give you an idea for a cool app: https://en.wikipedia.org/wiki/Cultural_Revolution https://en.wikipedia.org/wiki/Fall_of_the_Western_Roman_Empi...
First and foremost, use you analytic skill to assess if those protesters aren't just bunch of UIs used for somebody else benefit.
Hang on, are you asking about projects like the AI one that picks out violent protestors from the crowd via facial recognition or are you meaning software that helps protestors organise non-violent movements?
In Hong Kong, some people developed app showing "friendly" and "hostile" shops and restaurants.
If I were in your shoes, here's how I would approach it. You didn't mention a specific protest movement, so I will use BlackLivesMatter as an example.
I would first reach out to a local chapter of BLM to learn more about their short-term and long-term goals, and also probably try to attend as many events as I can.
The purpose of this would be to understand where the organization is going and what obstacles are currently stopping them. Then, maybe I can leverage my software skills to help.
But, it's important for me to first understand what the need is, because that's how you know you can have the most effect.
Maybe BLM needs AI facial recognition or maybe they just need a reliable CRUD app to reduce operational costs.