I think you can still go to a protest with a phone just fine honestly.
The fact that there are a lot of people there is actually the strength of it.
I’d probably think carefully about what you want to use it for and what I had on there though. I wouldn’t recommend bringing a device with a a bunch of incriminating evidence to an event like that.
I think a good threat model is just operate on the assumption that maybe someone stops you and asked to look at your phone. Go ahead and also assume that they will ask at the most inconvenient point in the day also. Act accordingly and I wouldn’t anticipate much in the way of trouble from having one.
Also, look at it through the eyes of the opposition, what are their goals here…
1. Fix the signal to noise ratio in a crowd
2. Identify people
3. Map out networks
And your goal is to not to be “invisible” (you can’t anyways) but to be uninteresting. They aren’t the same thing and the difference is important.
For the overwhelming majority of people I don’t think there is much yet to worry about in simply attending a protest (Assuming you’re a citizen and you act sensibly because otherwise that’s an entirely different threat model and you probably shouldn’t be there at the moment).
But I would leave you with this bit of advice also… they very much want you to think they are the all knowing, all seeing and ever present 50ft tall enemy. That isn’t true. There is also no shortage of people who really seem to get off on pretending things are more dangerous than they really are but that shit turns into paranoia real quickly and then people become terrified to do anything or you start making bad decisions. Fight both of those things when you run into them.
You can and should feel good about getting out in the streets at the moment, it’s not going to get easier the longer it goes on just be sensible.