I would not trust that any modern smartphone is fully off without yanking the battery.
Are you sure they don't have a backup battery or similar that can continue broadcasting your location after you pull the battery. That would be an ideal countermeasure as pulling the battery would be a great indication you may be about to do something "naughty" and you'd likely do such things shortly after too ...
That is not enough. Use a faraday cage.
Modern phones have two batteries [0].
Burner phones bought in cash from one of the little independent shops we have all over (here in the UK anyway) with pre-paid sims - not a new idea I saw it cropping up in fiction 20 or more years ago but still effective, used for a day or two and then dumped.
Isn't it tragic that the way you have to protect yourself from the state when organising a legal protest is pretty much the same way you would do it if you where a drug dealer or a terrorist (at least a reasonably smart one).
For the example of a protest march, if you're a participant or even a bystander walking home wanting to avoid being caught up in a surveillance dragnet, turning your phone off should be sufficient. You'd probably want to take stronger measures if you were involved in organising the protest, though.