Let's talk about taking phones to protests.

To start with the obvious, taking a turned on phone to a protest is a bad idea.

Getting a list of the phones - and thus, people - connected to nearby cell towers is trival. I assume you don't want to end up on that list.

You could just leave your phone at home, but then you deny yourself an useful tool. What if you'd need to urgently call someone? What if you want to record some police brutality?

Taking a turned off phone seems to be the best of both worlds - you can still turn it on during an emergency, but otherwise it won't be tracked back to the protest... or will it?

The lack of data is just another kind of data.

If you never turn your phone off, then any time you do so will be a clear outlier. While not as straightforward, it still doesn't take a genius to crossreference such outliers with the dates of protests. Thus, if you're the kind of person to worry about this, it's best to keep your phone off (or in airplane mode) as much as possible.

The more you avoid surveillance when you don't need to, the less you'll stand out when you do.

This logic doesn't only apply to mobile phones. For example, I'm a daily Tor user. I don't have anything to hide - but if one day I had to use Tor for something, that wouldn't be as suspicious thanks to my current usage. This also benefits other people. The more Tor users there are, the less each one stands out.

My point is: care about your privacy and surveillance in your day-to-day life. Even without clear benefits at the moment, it can benefit you (and other pepole) in the future.