It is easy to dismiss rebirth as a physicalist-materialist literalist, just as it is heaven and hell. But that shows a failure of imagination about why they have been such powerful psychotechnologies for millennia. And a failure to engage with the details of doctrine in their own terms, within a context of their function within the teaching.
"Intention (cetana) I tell you, is kamma. Intending, one does kamma by
way of body, speech, & intellect." - The Nibbedhika Sutta, Anguttara
Nikaya 6.63
Karma is about psychological cause and effect, not the allotment of good and bad results, but about how they are experienced - because our intentions are above all, attachments towards what we wish to experience.
"1. Mind precedes all mental states. Mind is their chief; they are all mind-wrought. If with an impure mind a person speaks or acts suffering
follows him like the wheel that follows the foot of the ox.
Mind precedes all mental states. Mind is their chief; they are all mind-wrought. If with a pure mind a person speaks or acts happiness
follows him like his never-departing shadow
"He abused me, he struck me, he overpowered me, he robbed me." Those who harbor such thoughts do not still their hatred.
"He abused me, he struck me, he overpowered me, he robbed me." Those who do not harbor such thoughts still their hatred.
Hatred is never appeased by hatred in this world. By non-hatred alone is hatred appeased. This is a law eternal.
There are those who do not realize that one day we all must die. But those who do realize this settle their quarrels"
-opening verses of The Dhammapada, an ancient collection of sayings of the Buddha, widely considered to represent the core of Buddhist thought
Buddhism can be understood as fundamentally a critique and reassessment of rebirth. One which reconciles that one of the three marks of existence is 'anatta', not-self, with the actions we take having consequences beyond our own lifespan - consequences not simply on the world outside of minds, but on other subjectivities. It takes the middle path between transmigration of an unchanging inner essence, and materialism that says death is the complete cessation of a person's life:
The king asked: "Venerable Nagasena, is it so that one does not
transmigrate and one is reborn?"
"Yes, your majesty, one does not transmigrate and one is reborn."
"How, venerable Nagasena, is it that one does not transmigrate and one
is reborn? Give me an analogy."
"Just as, your majesty, if someone kindled one lamp from another, is
it indeed so, your majesty, that the lamp would transmigrate from the
other lamp?"
"Certainly not, venerable sir."
"Indeed just so, your majesty, one does not transmigrate and one is
reborn."
"Give me another analogy."
"Do you remember, your majesty, when you were a boy learning some
verse from a teacher?"
"Yes, venerable sir."
"Your majesty, did this verse transmigrate from the teacher?"
"Certainly not, venerable sir."
"Indeed just so, your majesty, one does not transmigrate and one is
reborn."
"You are clever, venerable Nagasena."
-from The Questions Of King Melinda, Miln III.5.5. Canonical in Burmese Buddhism, a shortened version in some Mahayana cannon, and
widely translated and read in the Buddhist world. Dates to 100-200AD,
& said to be about events 200 years before
The details of the working of karma are listed in the Sabbasava Sutta as topics of 'unwise reflection'. Buddha states clearly that attachment to a self or to non-self, are both wrong views. I see this as drawing attention to understanding karma not as a machinery for how to get ahead, but as a way to understand that our actions have consequences, and how we use our minds can have lasting impacts on the minds of others.
In general Therevada Buddhist thought takes quite a literal view of the suttas. In Mahayana thought they have developed the psychological model of the arising of consciousness at the sense-gates, up to 'Alaya Vijnana' or Eighth-Consciousness or Storehouse-Consciousness, which I think can be meaningfully and useful related to the idea of the Noosphere, or Memesphere.
In Hindu thought there is far more diversity than we generally appreciate from the West, at least historically. Most positions of Western philosophy have been taken up by some school at some point, and the traditions that have survived generally have sophisticated answers on points of contention.
Advaita Vedanta, the oldest school of orthodox Hinduism, arose in large part as a counterpoint to Buddhist thought, focusing on the non-dualism of personal self called atman, with cosmic self Brahman. I see this as integrating the idea of the 'mani' or jewel-self in Indra's Net, the net of jewel-selfs reflecting each other and constituting reality, and Buddha-nature, the intrinsic capacity for freedom and attainment of a liberated mind. But, while juggling the language to keep respect for the Vedas, and securing continuity with wider Hindu thought and culture. The focus on sakshi, witness-consciousness, is distinct from Buddhist thought. But I would understand it as drawing a similar focus to attending to the possibilities of right now, which has a universal quality for all beings.
Of course many practicioners within traditions take a simplistic view of teachings about rebirth. And I would say that is exactly the point - rather than rewriting culture, using what is already there, to understand how to live better together, with an accessible form, and a deeper doctrine for those with more difficult questions. The fine details of doctrine are not for everyone. Buddhism in China has seen a pendulum swing between ascetic demanding Zen with few accessible doctrines, and extremely accepting easy to engage with Pureland Buddhism - to the extent most Zen schools honour Buddha Amithaba, who offers rebirth in a realm guaranteeing awakening in return for simply chanting his name; very like the promise of Heaven for the righteous. But the existence of a complex understanding that challenges ideas about the self, can allow problem solving by relating to the big picture, of what kind of world we are building, and what kind of minds within it. I go in to more details about the afterlife as being about what concepts or stories we grant symbolic immortality to, here: What are some philosophical works that explore constructing meaning in life from an agnostic or atheist view?
Avalokitesvara Bodhisattva is described as 'the thousand hands and eyes of compassionate action'. So we can understand at least for Bodhisattvas, that the self and rebirth is not limited to being in one place at one time.