If you don't want ICE to know you were at a protest, taking a burner phone is not going to help you stay anonymous if you go home afterwards. https://www.404media.co/inside-ices-tool-to-monitor-phones-in-entire-neighborhoods/
There are other reasons you might want to take a cheap/disposable/burner phone to a protest, such as making sure that if you are arrested, the police don't seize/break/confiscate your main phone.
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