I'd recommend you don't sign anything at a protest, ever. No petitions, no signing up for orgs, not even if a goth baddie asks you to sign their tits. Do that stuff offsite before or after a protest on your own time where's it's a lot less likely to be an informational gathering tactic. You don't want a record of which protests you've been to, especially if they're the spicier kind where direct action might be happening.
Mask up and bloc up.