Re: Buddhism

 Buddhism isn't just a "philosophical way of life":

• According to the South Asian tradition, it is a nastika ("non-orthodox", i.e. not accepting the Veda as authoritative) darshana (vision of the divine, glimpse of the numinous).
• According to the East Asian tradition, it is part of the sanjiao (three teachings), an aggregation of belief systems undergirding the stability of the Chinese empire and by extension the whole world.

Regarding the core tenets, Buddhism qua adhering to a karmic conception of being is in a fundamental friction and disharmony with worldviews adhering to a conception of being rooted in grace. Therefore, there seems to be an essential and materially underlying gap between Buddhism and Christianity.

Moreover, I'd assert that reincarnation and karma are direct and essential corollaries: Karma is the (for lack of a better term) "subjective" instantiation of (and also for lack of a better term) "objective" dharma ("cosmic law", "natural order"). Wherever karma and dharma deviate from one another in a particular fashion, be it in a "positive" or "negative" way (= good and/or bad karma), there is a subjective individual - an alleged "self" whose substantial being is but an illusion. Now, as long as such a particular deviation between karma and dharma exists, there is an individual alleged "self". And if it loses one specific shape (for example, if a human dies) that particular deviation still continues to exist and simply adapts to another shape. This change of shapes, eventually, is conceptually referred to as "reincarnation". Which is why the ultimate goal in Buddhism, for example, is not the gaining of a massive amount of good karma, but the nibbana, the complete eradication of any particular karmic deviation in order to escape this eternal cycle of changing shapes (samsara).