Every transaction is recorded forever. What's anonymous about that?

Anonymity is about names, not about records.

You've just shifted the problem to "how to I buy bitcoin anonymously" because all the easy and obvious ways involve disclosing your name.

That means, that if the organziation hasn't setup an crypto address (is this the correct term?), I cannot donate?

You could always spend a few bucks and get a Visa Gift Card.

That's a simple and easy solution. I will try it out the next time, thank you!