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.
But if it is important to you to maintain your anonymity at a protest, consider leaving your phone at home, or at least turning it on/off only once you are well out of the neighborhood.
If you have a fediverse account, you can quote this note from your own instance. Search https://hachyderm.io/users/evacide/statuses/115864043539732413 on your instance and quote it. (Note that quoting is not supported in Mastodon.)