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MITRE maybe? They're a US government-supported non-profit R&D company.

Kind of but they're really a government agency in essence, no? I mean that's like calling In-Q-Tel a nonproft, really it's just the CIA's venture arm in a nonprofit shell for legal/management reasons

I think lots of nonprofits have public welfare in their mission but I think by organization you mean for profit entities? In that case my answer is the same as to the one for VCs in that there are lots that care about society and specific sectors and have that as a thesis with returns being equal (or perhaps secondary for a select few); climate tech startups and investors for instance or companies making alternative proteins (although maybe that's "animal society" not human that they care about)

Mackenzie Scott (formerly Bezos), although her approach is about as far removed from traditional VC as one could imagine.

Wikipedia, EFF, Gnu