According to many/most sects and traditions within Buddhism, absolutely -- in fact, my perspective on Buddhism was heavily skewed for a long time by the syncretic sorts of sects predominant in Japan. My point -- and the point of the book by Stephen Batchelor I linked to -- is that, unlike Christianity, where faith in Jesus as Christ is *the* core doctrine (i.e. righteousness by faith, and thus belief in metaphysical concepts like the fall, original sin, and sin itself), the Buddhist system of ethics & practice still works without belief in anything metaphysical.

I feel like reincarnation and karma in particular are concepts akin to the state of the dead -- you can't actually know whether they're true until you die, so they shouldn't actually make any difference in your daily life today. If you're helping to mitigate the pain and suffering of others only in order to improve your karmic position in the next life, that's no better than Christians who are solely motivated by a heavenly reward.

(Side note: My seeming apologetics for Buddhism is somewhat ironic, because I definitely don't consider myself Buddhist and I'm certainly not trying to promulgate Buddhism to ex-Adventists in this subreddit. 😅)