I recently attempted to make an anonymous donation online. It was a bit of a pain, here's how it worked for me.
1. Purchased a Walmart gift card in cash at the store ($50, $4 purchase fee).
2. Registered card on Walmart website. I tried to use Tor, but got blocked at the Captcha test -- for some reason Tor is often incompatible with Captcha. I ended up registering with Firefox -- after the fact, it occurred to me that I may have been able to route my Firefox traffic through Tor. I used the store's address as my "billing address". Even though Walmart claimed that the card was activated immediately, it took a few hours before their website recognized it as an active card.
3. Created an account on Patreon (the recipient was using Patreon). I used a pseudonymous email address for this -- I expect this email could be tracked back to me with a little effort, but I don't expect anyone would expend that effort. I'm only slightly concerned at repercussions from this donation -- not due to current laws, but due to a growing disregard for free speech, such as with the anti-BDS laws. I was able to create the account using Tor (but not on the first attempt for some reason).
4. Paid Patreon using the gift card. For some reason the Patreon website did not allow me to enter the card's number using Tor, so I switched over to Firefox. Now that I've set up the payment, I'm switching to contacting Patreon with Tor.
5. Potential problem: The gift card is not supposed to be used for recurring payments. I set up a small monthly donation. We'll see if it gets rejected next month. It would be nice if I could transfer all the money to Patreon or another intermediary, and then pay it out a bit at a time, but I don't know if that's possible. I see that Patreon accepts PayPal as a payment source, and I think they let you keep an account. So maybe that would be the way to do it.
End result: Not very effective. Probably not worth the time (except as a exercise).
1. Patreon knows who I donated to, and they have my IP address and my pseudonymous email -- and my Walmart gift card.
2. Walmart has my IP address and knows where I bought the gift card.
3. The recipient has my pseudonymous email.
I'm most concerned with Patreon as a weak point -- I can imagine an antagonistic entity forcing them to release their payment records, and then opening a file on everyone who has donated to targeted organizations. But even in that case, they would have to do some extra work to figure out who I am (though maybe contacting my ISP would be enough).
(this post was composed through Tor browser)