First, let's remember that psychoanalysis is highly speculative, hence we get people who believe Freud was correct, while others reject him.
Jung, and others, believe there is evidence for a collective unconscious which stems from shared experiences or images from our ancestors, going right back to the beginning. Certain things persist in the human psyche, such as the Tree of Life. It is primal.
Because you have raised the question of religion's role, it is therefore appropriate to invoke Jung who argued that we retain this innate knowledge that is shared by the entire human race. It may be suggested that the myths that succeed in humanity are the ones that resonate to that collective memory (although it is not overt memory.)
So, the same Eastern metaphysicists (who should be called Western Adopters, as they have indeed sacrificed their culture to adopt Eastern Mysticism), would have to embrace Jung's concept of the transcendent, as it is in harmony with the notion of the connectedness of all life and the recurrence of the soul.
As science, it is very difficult to prove conclusively. However, I remember in college studying an experiment alleged to have evidence of the collective unconscious. Planarians (primitive flatworms) don't actually have brains in the sense that mammals do, more like they have nervous systems that meet that need without a big computer. The experiment shocked the planarians when a light was introduced, and the worms "learned" to associate pain with the light. There is no natural fear of light in planarians. The creatures soon developed a Pavlovian response to the light, and recoiled in anticipation of pain
before any shock was applied or even if not applied. But the bizarre thing is that the next generation of planarians exhibited the same reaction to light even when they had never been shocked ever: they recoiled from an experience they never had directly.
The paper from 1965 is here:
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0ahUKEwiij7vL0p7SAhUM74MKHYK7AG0QFggcMAA&url=http%3A%2F%2Fase.tufts.edu%2Fbiology%2Flabs%2Flevin%2Fresources%2Fdocuments%2FPlanarianManual.pdf&usg=AFQjCNHuNu837ylPQBhgQjAO3i4wAhOfaA&sig2=OG42ZKYldqRVmXlFrt2B7g&cad=rja No doubt, as in all research, there are refuters and rebutters, but it is a fascinating premise.