In his article "Contestation and Consensus: The Morality of Abortion in Japan," William R. LaFleur makes the connection between beliefs about the afterlife and attitudes about abortion. Because of the prevalence of belief in reincarnation, there is a common attitude in Japan that while abortion is sorrowful it is not morally wrong. The soul of the child goes on in the process of reincarnation.
In her article "On the Moral and Legal Status of Abortion," Mary Anne Warren does not explicitly link beliefs about the afterlife and attitudes about abortion. However, her definition of what it means to be a "person" is thoroughly naturalistic, and connected with the belief that there is no afterlife, that death is the end of the existence of the child. Indeed, her definition of person leads her to argue that since the third trimester unborn child is similar to the infant, Mary Anne Warren argues that infanticide is morally acceptable although not culturally acceptable at this time.
The relationship between beliefs about the afterlife and beliefs about abortion is important but overlooked. It formed part of the Roe v. Wade deliberations. When "specialists" were asked about the existence of the human soul, but conflicting answers were given, the conclusion was drawn that such considerations are unknowable and cannot have a bearing on the case. Instead, privacy and the right to privacy became the central concern. Since no one has the right to privacy in killing another human, the implication is that the unborn child is not human. Consequently, the subsequent debate over the past decades has been about when the child becomes a human.
Besides the beliefs in reincarnation and "when you're dead you're dead," there is the heavy influence of Plato's otherworldliness in the West. This can be found in Plato's Republic book 10. It teaches that the body is stuck in a soul, and at death is freed to go on to what we call heaven. Plato does speak about a judgment after death, and in this respect his view of the afterlife might not encourage abortion. However, Plato's belief about the soul is that it achieves the highest good after it leaves the body. Similarly, the popular view of heaven is that a person goes on after death to achieve the highest good. Thus, there is an attitude which expreses itself in a similar manner to the reincarnation attitude above, in saying that since the child would have had a hard life it is better this way. The body is not needed to achieve the highest good.
By way of contrast, there is also the belief in the resurrection of the dead. This view maintains that humans are a body/soul unity, not a soul stuck in a body. Thus, at death the body and soul are separated, but the soul awaits the resurrection which occurs at the end of history once good has overcome evil. This view of the afterlife is antithetical to abortion in that it maintains: i) in contrast to reincarnation and heaven human life as a body/soul unity is valuable and the body should not be discarded; ii) in contrast to naturalism/materialism a person is forever, meaning that even if we kill someone now, we will be confronted by them again in the resurrection and asked for an accounting; iii) the highest good for humans is achieved as a body/soul unity, not in escaping the body and going to heven; therefore, the child that is aborted is bereft of the valuable opportunity to be part of human history.
Since the existence and status of the human soul is relegated to the unknown/unknowable, it is not surprising that the abortion debate still rages with strong feelings on both sides. To simplify: If the death of the body is the end then abortion is no big deal; if the person is forever then abortion is a big deal. Culturally, we do not seem to have the method in place for dealing with these kinds of questions. Indeed, I'd argue we've set up road blocks to keep ourselves from having to deal with them. The most common is the claim that such beliefs are personal and should be kept out of the public sphere. Of course it is true that beliefs are personal, but it is also true that the public sphere will be influenced by beliefs. It is unavoidable. The question is whether the public square will be influenced by reason and argument or something else.
The articles I considered above should make us consider our own thinking on the relationship between beliefs about the afterlife and beliefs about abortion. If we can't know either way, how can we "err on the side of safety," and is that the present model or not? If we can know, why have we avoided this?