Somebody mod the biologist here! That's it right there!
No sane environmentalist judges extinction to be unnatural in the platonic sense. Extinction IS a direct effect of natural selection. That doesn't mean we should just "get over it" or any other dismissive crap that usually appears in the same sentence with "you damn hippies" or "humans are nature too" or "the climate has been hotter than this in the past." We care about the Sumatran Rhino becoming extinct because we like the world better when it has the Sumatran Rhino in it, not because we have some hang-up about extinction itself.
I have no problem at all being selfish about this: the world is a nicer place for me to live with a healthy ozone layer, fresh air, old growth forests, thriving oceans, and Sumatran Rhinos. Don't try to tell me I'm a hypocrite because the environmental problems we're experiencing today are "natural." I'm not even going to tackle whether or not humans caused all these problems (hint: we did), I'm just going to say that it's perfectly ok to want species to live, even spend time and effort helping them to survive because they are valuable to us. No extra points for true altruism here.