As you approach the danger zone, search your person for any electronic device, functional or otherwise. Earphones don't have to be plugged into anything. Just stick them in your ears and start rocking out to your imaginary music. Double points if you've got nothing playing. Then you can listen to their useless pleas as you walk casually past. If you don't have earphones, go for the cell. Make the imaginary conversation about something awkward and embarrassing to ensure that you're not accosted.
And the Oscar Goes To ...
This one is easy if the petitioners have set up near a campus and you look relatively young. Hurry your step until you look like an agitated, power-walking middle-aged woman, minus the frightening spandex. Look at your watch or cellphone as if in the deepest distress. If the petitioner is on campus and asks if you're interested in reducing greenhouse gases, you can look at the sidewalk and mutter "Sorry, late for class." Otherwise you can look up, let a single tear leak down your cheek and whisper "Mom loved greenhouse gases." Then break into sobs and hurry on your way.