I am interested by the way in which Sheldrake develops his ideas to explain past life memories. It is consistent with the understanding of past lives by some Buddhist thinkers in which there is more of an underlying continuity of past life forms as opposed to concrete entities and in line with the fluid conception of self. The mistake which some people may make in querying past lives is to think it involves the specific stream of narrative personal identity, or the ego consciousness.
The general understanding is consistent with the relationship between a person and 'other minds', including ancestors and other living people. It is likely to involve a web of system interconnections. This would link with the idea of a collective unconscious, or to choose another philosophical term, intersubjective relationships in nature. It involves the evolution of consciousness in nature.
Some people may grow up with vestiges of past lives. I read, 'Past Lives, Past Masters', by Andrew Weiss, in which he, with no previous belief in reincarnation undertook the hypnotherapy of a patient. It involved the revelation of detailed memories from past lives, leading Weiss to consider the nature of past lives seriously. He ends up concluding that it was unclear if it was based on actual lives lived by the woman and himself or the tapping into the collective unconscious.
I am not sure why the idea of the collective unconscious is rejected by so many. It is at the juncture of 'science and spirituality', as you suggest, and this may be where it seen by many as problematic. I am extremely influenced by Carl Jung's ideas, as you and others on the site may be aware. I don't know why the ideas of Jung are seen as pseudoscience because they give a more flexible idea of 'mind' than many other approaches.
Jung draws upon ideas which may be seen as 'supernatural', which was the objection of Freud, but he does also draw upon ideas of biological naturalism. The idea of the collective unconscious is neither completely biological materialism or idealism, possibly fusing them in a complex way and drawing upon the Platonic idea of archetypes. I found the writings of Anthony Stevens helpful here because he traces such ideas in relation to biology as opposed to some 'supernatural' thought.
Even the idea of the supernatural is open to critical scrutiny, as argued by the biologist, Lyall Watson, in his 'Supernature', who sees the whole approach of extrasensory perception as being problematic when seen as 'paranormal', as opposed to being about the complexity of 'minds' in nature.