Have they ever tried crowdfunding campaigns? I don't think so. Wikipedia seems to be doing fine with it. At least they should experiment with some ideas in that line and see what works.
Wikipedia has sufficient marketshare to survive despite that.
The ads that mozilla shows are fairly privacy-friendly, much more than any other ads you'd find on most websites. That's an improvement.
If you don't like them you can easily disable them.
Users may not like nag screens, but I doubt they like the shitty ads Mozilla shows on the new tab page by default either. As long as the screen is easy to dismiss I don't see the problem.
Wikipedia has, as mentioned, the market monopoly advantage so they can do as please, Firefox doesn't and can't afford to annoy users.
I would doubt users are more annoyed by ads, especially the type of ads that Mozilla uses, than nag screens.