I've moved to Team Iron Man and Anti-Registration Influence is dropping for me instead of Pro-Registration. This seems to happen in Midtown, Cosmic Midtown, and terminals (green and cosmic). This includes disturbance intel reports. HOWEVER it does not include the daily quest given by Maria Hill to destroy 15 boxes in Kingpin's hideout.
I ran that daily thinking that maybe I needed to complete that to start getting the influence. After getting that 40 Pro-Registration Influence and right clicking on it to see it go to the shield requisition agent, I checked back into Cosmic Midtown and went right back to getting Anti-Registration Influence.