@Lyndon thought you a western Buddhist. I'm not clear yet. What kind of reincarnation do you believe in?. Does it include a reincarnating individual soul? Or what?
I have found that many western Buddhists n RF define 're-birth' in such a way that it can still be compatible with materialism.
I have not defined Reincarnation definitively yet, instead I like to make different theories based on the basic idea that
something in the reality fluctuates through transformation and through arising and disintegration.
I do not flat out completely reject the idea of a reincarnating soul, based on the fact that I don't know for certain if its true or false, but I tend to dismiss it personally as I give greater emphasis to both Anattā / Not-Self and Suññatā / Emptiness. I do lean towards the position that reality is ultimately a product of cosmic creativity, which could very well be a sort of world-consciousness. So while my understanding of reincarnation is in turn informed by my understanding of Anattā and Suññatā, I do hold some views that go hand-in-hand with traditional Dharmic understanding.
There are three main 'theories' that I formulated and hold regarding the basic idea of transmigration of the reality-essence:
(1) The Physical Transmigration.
This is arguably the materialist understanding. Everything in the physical reality arises and disintegrates, rearranges and transforms and arises and disintegrates again. Different iterations of the same essence, repeating and transforming, ever since the world blew into existence. Thats one way to see Samsara, and I don't think its false just because it has a materialist viewpoint.
(2) The Idea-body Transmigration.
This is arguably the psychological understanding. Reincarnating could be seen as ideas and personality-fragments circulating throughout the social realm: the doctrines that we accept and allow to shape our worldviews, the ideas we learn and accept from others, the behaviors that we come to emulate, the compulsions that transmigrate as idea-behaviour patterns...they all are exchanged by people all the time. When we inherit somebody else's worldview, you could say that there is a 'little rebirth' right there - and in Buddha's words, the new iteration would be "not entirely different, but not entirely the same" as the original. And, often this idea-body transmigration is very clearly driven by desire, clinging and skillfulness, just as Buddha espoused.
(3) The Consciousness Transmigrating.
This is arguably the idealist understanding, and the one found in traditional schools of Buddhism and other Indian religions. That is that there is one whole cosmic consciousness / cosmic creativity that reincarnates throughout reality. The idea is fairly simple and accepted by myself. I don't attribute personality to this cosmic consciousness, though, as personality is something that arises in conjunction with bodily senses and experience. A cosmic consciousness would not have these.
However, I do think that all these three 'theories' can coexist and I personally hold them all as valid. If there is a cosmic consciousness / cosmic creativity, then everything, including the physical realm and the human ideas, are a by-product of it. Therefore, they are not three separate viewpoints as much as they are three aspects of one viewpoint. The Western Buddhists who like to focus on (1) or (2) instead of (3) just focus on a different aspect of the Buddhist reality. I tend to look at all three and hold all three as personal views of mine, mutually valid, but for Buddhist practice and pursuit of Nibbana I feel that (2) is the most crucial.