My answer for Buddhism is that if one subtracts the beliefs in karma, rebirth and nirvana, what remains is a philosophy that should be attractive to contemporary analytic philosophers. “Buddhism naturalized” contains a powerful and credible metaphysics, epistemology and ethics. The metaphysics is an event or process metaphysics. There are no things, only events that unfold in a great beginning-less unfolding, the Mother of all Unfoldings. The self is one of the impermanent events. The epistemology is empiricist: experience first, then reason and only then do we consult the “scriptures,” which are themselves fallible compilations of wisdom from previous experience. The ethics teaches that goodness comes from compassion and Lovingkindness to oneself and to all other sentient beings.Flanagan is a balanced and rational commentator on Buddhism and other wisdom traditions, and I agree with him that these have much to offer for modern secularists (and, I would add, adherents of Abrahamic faiths as well). However, I wonder whether subtracting karma, rebirth, and nirvana from Buddhism leaves one with Buddhism at all, or something else entirely. This is not to say that we should retain these outmoded elements of Buddhism, but rather that perhaps we should abandon the label 'Buddhism' altogether. Less radically, adopting a term like 'Neo-Buddhism' (akin to the already current neo-Aristotelianism and neo-Confucianism) might make more sense then referring to naturalistic Buddhism as 'Buddhism' in an unqualified sense.
I believe that “Buddhism naturalized” is a serious contender, along with Confucianism and Aristotelianism, for a great wisdom tradition that offers a viable philosophy for 21st century secularists. It might seem odd to recommend these ancient theories as good for us now, but I do really think all three are worth a second look. The reason is that all three of these philosophies, from over 2 millenia ago, are less theistic, and thus more rational, in their core philosophy that the three Abrahamic traditions.