Is it permissible to give Maaser money (or for that matter, a large sum of spontaneous Tzedakah), to an animal protection or endangered species charity? Would this be considered foolish spending or a mitzvah?
You are a very caring person, and have much feeling for those poor animals. You can donate money to help them if you want, however it can not be from maaser money. This is because maaser money is meant specifically for poor Jews.
Not halacha per se, but I found a really nice explanation from the Orchos Tzadikim (14:19). The Orchos Tzadikim writes:
He asked Melchizedek, "How did you emerge from the Ark?" And Melchizedek answered, "Because of the charity that we did there," Abraham said to him, "What kind of charity could you do in the Ark; — were there any poor people there? There was no one there except Noah and his sons, so to whom were you doing charity?" Melchizedek answered him : "With the animals, with the beasts and with the fowl. We did not sleep but were constantly giving food to all these living creatures all night long." (emphasis mine).
A huge thanks to @Dov for pointing out that this was taken from the Midrash Shocher Tov (Midrash Tehillim 37:1).
So, according to the above, and also the article from Dinonline, it should be a "humanistic" thing to care for the animals that need it. Just as it was done in the Ark of Noach. However, to do it with maaser, is not allowed. As I recall correctly, maaser is only allowed for persons in need, not animals.
See also Halachipedia, section Whom To Give To:
Definition of Poor
Someone who is lacking basic needs for him or herself or their family