so where was his "strong anti-authoritarian and anti-military streak" when he was rolling over for the NSA **for years**...
That never happened. The NSA tapped Google's fiber without Google's knowledge, but there's no evidence that Google ever willingly participated. As soon as Google found out about the taps, it accelerated a program to get the data on all those fibers encrypted, to lock the NSA out.
Google invades privacy for profit and for decades gave the NSA (and god knows who else) an unaccountable back door to all our data
Google trades the right to target ads to you in exchange for services, and enables you to opt out of the trade if you want, even providing the necessary tools for you to do it. Google has never given the NSA an "unaccountable back door". See David Drummond's numerous public statements on this issue. From my personal perspective as a Google security engineer, I think it would be virtually impossible for such a back door to exist in Google's systems without my having noticed some trace of it. Take that as you will.
You're coming to this question with a whole bunch of inaccurate assumptions, which are seriously skewing your perspective. You should take a breath, look into what really happened (as much as is public information anyway) vis a vis the NSA, PRISM, etc., and then re-evaluate.
Or not, that's your choice. I'll merely point out that time will prove me right with respect to any purported military-focused work by Google X and leave it there.