What annoys me the most is that I've been donating to Wikipedia for over a decade and I still got the plea message, but if I click that little X button I don't see it anymore. Big deal.
Wikipedia's tactics here have long been very scummy. They're a charity not a company, so people's guard is down due to the incorrect belief that charities don't have/care about profits. And the claims they're making aren't of the subjective type you learn to ignore in advertising - they tend to strongly create the impression that they're in dire poverty and Wikipedia might shut down if they don't raise enough money, which is just flat out untrue.
Frankly, I'd rather have advertising than this situation. Advertising can be annoying but it wouldn't create a culture of dishonesty at the Wikimedia Foundation, as relying on donations has apparently done. Especially for an encyclopedia organization, honesty and trustworthyness are some of their most important assets, and every time they do this they set it on fire.