The Radiation Can Be Deadly
On ebay.com, search for "Faraday bag cell phone". There are lots to choose from. Many cost under $10 (more like $4 if you buy 3). Consider putting your device in a Faraday bag (which blocks all radio frequency energy) when you are out and about and don't want to be tracked.
Note that "airplane mode" doesn't turn off all the radios on all brands of phones. If you can remove the battery, that is best, but if not, then a Faraday bag is worth having.