If one is to go this road, one may consider the model of the boycott organizations structured by the NAACP---how they designed them, how they enforced them.
Practically, the hard power any such organization is going to have would start with their spending dollars (and possibly their signal... A lot of Google's "special sauce" is big data from big usage, and if usage goes down, software quality suffers). Google would (and does) listen to a significant percentage of their dollars-base saying "Change this or I'm taking my ads to Facebook and my infrastructure to AWS." They may perhaps listen to a significant percentage of their user-behavior-base saying "Change this or I'm using Bing," though it'd have to be a hell of a large organization to make a dent.
Practically, the hard power any such organization is going to have would start with their spending dollars (and possibly their signal... A lot of Google's "special sauce" is big data from big usage, and if usage goes down, software quality suffers). Google would (and does) listen to a significant percentage of their dollars-base saying "Change this or I'm taking my ads to Facebook and my infrastructure to AWS." They may perhaps listen to a significant percentage of their user-behavior-base saying "Change this or I'm using Bing," though it'd have to be a hell of a large organization to make a dent.