It might not help you as it seems you might be in the US, but I regularly donate to MIND (a UK mental health charity), mermaids UK (A UK trans youth charity), Stonewall, and Greenpeace. I think they're all awesome.
I also support the Awesome Socks Club, which isn't really a charity donation but they're donating 100% of profits to various charities, they said they're trying to beat Paul Newman's company's charitable contributions which is a huge effort, it supports independent artists, and you get cool socks to top it off. (www.good.store)
I've grown disillusioned with Greenpeace, they seem to have lost their north a long time ago, and only hop onto the bandwagon of what's cool at any given moment. Like, "no fossil, no nuclear, no global warming" are all cool and all... but a contradiction. Or the silliness they're doing right now in Spain, of combing whole beaches to remove a few pounds of plastic pellets from each... only for more to come the next day... while 30-odd years ago we already used to wonder what were all the multicolored "sand" grains, and some kids used to pick up chunks of tar to chew like gum.
I would suggest either Extinction Rebellion, which has an interesting open governance system with local chapters, and is "effective" in the sense of pissing people off enough to get itself on TV... or any local charity focused on a single achievable goal (sifting plastic pellets from a multi-ton dump at a rate of a few pounds per day, is a populist waste of resources; reforesting some area with native species, is direct and effective; and so on).
You're right-- I am in the States, but your input is still welcome!
I don't have an Awesome Socks subscription, but I do have a Sun Basin Soap one with good.store! I like Daydreamer, even though it sorta reminds me of allspice (and therefore chicken).