OP
While I'll stand corrected about rogue employees misusing data, Google itself does give it out users' personal information to the NSA,
Again, what has that got to do with Google and my banking data or my personal information? If the NSA wants my banking data, they're not gonna be asking Google. Google cooperating with the NSA has exactly nothing to do with the topic. If the NSA wants my personal information, Google ain't gonna stop 'em from getting it.
The discussion is about if I'd trust Google to do banking in Chrome/Chromium and with my personal information. The answer is, "Of course." Google cooperating with the NSA isn't going to change that. I can't imagine why you'd think that'd matter. (No, the NSA doesn't care about you either.)
For the record, I don't like the NSA spying on American citizens. Also for the record, that's gonna impact me exactly none.
I'd trust Google to keep my personal information pretty secure. It'd look bad if they didn't. There's no real motivation for them to share it with anyone else - while there's lots of motivation for them to gather it.
They don't care too much about the individual, they care about the aggregate. E.g. What interests do I have and how can they exploit them to sell me more products? They're not gonna go skulking about and stealing my money. Oh no! They might tell the NSA that I searched for ways to encrypt a thumb drive!
While we're at it... No... No, the big ol' bad government doesn't scare me either. There's pretty much nothing they can (realistically) do that's going to meaningfully impact my life in one way or another. It's statistically unlikely that they'll randomly charge me with a crime. I don't do anything interesting. I pay my taxes.
No, I'm not worried that they'll come take my rights. No, I'm not worried that they'll come take my firearms. No, I'm not worried that they'll target me for anything nefarious. No, I don't live in fear. I assess probabilities and adjust accordingly. I don't 'trust my gut', I trust data and facts.