Today I've been thinking about ways an open source project would be able to accept donations (that they absolutely need, in many cases) without compromising on the ethics and the project values.

Let's say you're making a cool important thing, and a megabucks corporation offers you a million (or ten, or two hundreds) USD a year in exchange for a link to their website somewhere in your PR materials (website or the thing itself). I think being open to such offers will likely have negative consequences. Maybe you'll get some bad actors trying to bribe you, and even rejecting them will have negative consequences. Maybe your old sponsor will drop "don't be evil" and will sponsor genocide. What do you do, then? How can you prepare for such an event, assuming that your project is big enough to attract such sponsors?

I can't think of anything better than only accepting anonymous donations, with some policy provisions to protect the integrity from "big sponsor threatens to stop the donations". Any other ideas?