But still there are plenty of anti-supernaturalist atheists around who consider themselves Buddhist. Perhaps they are working within a different tradition of Buddhism where supernatural beliefs are absent or deemphasized. Or perhaps they're picking and choosing from Buddhist traditions, taking only the parts they like.
There are some Buddhist traditions that I like too. I like the idea of emptiness, and the idea that there is no constant self. I think this is true to reality, or about as true to reality as an ancient belief can be. I am not the same person I was or will be, I merely share some attributes. Most (or all) things are not really things at all, but patterns. There is nothing underneath.
But I'm pretty sure there's more to the Buddhist idea of emptiness than that. And there are plenty of other non-supernatural Buddhist traditions that I just don't care for. Like meditation. Or the Middle Way. Or framing the world in terms of suffering and enlightenment. None of that stuff's wrong per se, but it just doesn't appeal to me as a way of seeing the world.
The choice for me is easy: I will not identify as Buddhist. But if you're into all those Buddhist beliefs and practices, minus the supernatural parts, you might be justified in identifying as Buddhist.
Here are a few things people said on Friendly Atheist about being both Buddhist and atheist:
Yes many people who are Buddhist today believe in supernatural things. However at the base of Buddhism, it is just philosophy of how to live your life.
I really don't view Buddhism as a religion. Instead, I understand it to be more of a lifestyle or philosophy; one that can be easily adapted into any belief system or lack there of.
The early Buddhist texts, particularly the Pali Canon, are free from all the woo that seems to have come later.
There is a sutra in the Pali Canon where the Buddha basically states that it does not matter whether rebirth is real or not.I respect people's decisions to identify as Buddhist, but I disagree with some of these specific comments. If we see Buddhism as a philosophy, to be judged on its merits rather than on its authority, I don't understand why people feel the need to defend "original" Buddhism. Gautama's Buddhism is no more authoritative than later developments. For example, the concept of "emptiness" that I like so much actually appeared some six centuries after the origin of Buddhism.
I think people refer to the supposed naturalism of "original" Buddhism because they are trying to establish that Buddhism is at heart a secular philosophy rather than a religion. But I disagree with this view, because I think Buddhism, like all other things, has nothing at its heart. It is empty, without any central essence to represent the "real" Buddhism. In other words, atheists can be Buddhists, but they are no more legitimately Buddhist than the ones with supernatural beliefs.
Buzzfeed once did a video "If Asians said the stuff White people say", which I think is relevant to the topic.
At 0:50, a guy says, "I'm really into western religions lately. I love how they're so angry and uptight, you know? I decorated my whole house in crosses!"
I wouldn't say that it's appropriation, exactly, to take ideas from Buddhism that you like. It wasn't "appropriation" when Filipinos adopted Catholicism, it was just conversion (and colonialism). Buddhism is an idea that wants to spread, so there's nothing wrong with having it spread and transform across cultures.
However, I suspect that if there were more Buddhists in our culture, atheists in the US wouldn't be so quick to say that the kind of Buddhism they practice is the real Buddhism.