Don’t trust the surveillance device to turn off because you ask nicely. Leaving it at home helps sell the idea that you weren’t at the protest you were at.
Do you actually know anything about software or are you just saying things
If you have an iPhone you can go ahead and try Flight Mode right now. You’ll see that it disconnects from WiFi and disables cellular. NFC, Bluetooth and Wi-Fi stay powered on, Bluetooth stays active. Yes, latest iOS has Bluetooth tracking protection on by default (varies by country, illegal in some), but it is not completely safe. I’m not sure about NFC and Wi-Fi. If you power the phone off it is unlikely to turn off the radios - they are needed for “find my iPhone” and similar features on Google and Samsung Galaxy phones.
Overall you can’t be confident that your phone does not reveal your location and identity to “law enforcement”, especially in places where police is well equipped to track you.
I’m pretty sure the SIM still connects to cell towers even if you have mobile data deactivated
Edit: on most phones it prevents the connection but there are still other ways to track like GPS
