So let's say the googlers who are against their labor used in this fashion are just a vocal minority and the rest of the folks are largely ok with it and are simply quiet. What should happen?

If they're simply quiet, obviously they don't care that much whether it happens or not?

I think there is a silent majority of people who are frustrated by the ongoing politicization of the workspace. They are quiet not because they don't care, but feel that it's rude to be so "loud" at work.

There could be a democratic structure in place where employees can elect internal representatives to conduct things and advocate for/against issues on their behalf; alternatively (and more Google's style) there could be a direct democracy vote on particular issues.

Wouldn't the most Google style thing be... "Liquid Democracy with Google Votes" [1] ;) ?

The deep question though is: should employees of a corporation have a say in its governance ?

Views from anyone in Germany would be interesting, as they seem to have a particular system for this. [2]

[1]: https://www.youtube.com/watch?v=F4lkCECSBFw

[2]: https://en.wikipedia.org/wiki/Codetermination_in_Germany