This is one of those questions that is complicated by that in the United States the conversation around abortion looks and feels very different than it does from other countries in the world. It is also made complex by the interaction of the ideology and the "situation on the ground," where things are usually quite complicated.
To quote Karma Lekshe Tsomo's excellent article Prolife, Prochoice: Buddhism and Reproductive Ethics:
In Buddhism, a primary guiding principle for ethical decision-making is the relief of suffering. It is clear that both abortion and restrictive abortion laws can cause great suffering for both mother and fetus. […]
In the end, most Buddhists recognize the incongruity that exists between ethical theory and actual practice and, while they do not condone the taking of life, do advocate understanding and compassion toward all living beings, a lovingkindness that is nonjudgmental and respects the right and freedom of human beings to make their own choices.
So to start with, we need separate "pro-life" (in the sense of being opposed to abortion) and "pro-choice" (in the sense of believing the state should restrict it). There are certainly Buddhists who are both pro-choice and anti-choice regardless of whether they are also "pro-life."
It is widely recognized in a variety of sources that, in the traditional Buddhist sources, the ensoulment occurs at conception. Bhikkhu Bodhi mentions in the book In the Buddha's Words that consciousness (or perhaps more precisely viññāṇa) begins "from the moment of conception," though I don't know where precisely in the texts this is defined to be the case.
We see that this translates to a "pro-life" and sometimes "anti-choice" attitude in the Theravada countries. Sri Lanka allows abortion to preserve the life of the woman but not for any other reason. Myanmar is similar. Thailand is slightly more permissive–especially since it allows for health of the mother under some circumstances and includes mental health–while still generally banning it.
In Peter Harvey's An Introduction to Buddhist Ethics we see analysis that indicates that:
It is clear, at the very least, that the great majority of Buddhists agree that abortion is killing a human being, and is an evil that should be avoided, other things being equal. A crucial issue, though, is how evil it is and what 'other things' can come to outweigh this evil, so that abortion comes to be seen as a 'necessary evil' in certain circumstances?
It is important to note that in some cases these laws were only written after contact with European societies (details in links, Peter Harvey indicates as well that, pre-colonial times, Burma/Myanmar "abortion was not liable for punishment"). It is also the case that, even where it is banned, the laws do not appear equivalent to murder. There's also a great deal of individual variation outside of the state laws, especially in Thailand, where 95% of the population is Buddhist but there's some popular support for more lenient abortion laws.
As far as I can tell, Tibetan Buddhism is similarly strongly opposed to the practice, but there's still some nuance around treating it, with the Dalai Lama saying in an interview with the NYT (from the above BBC article examining Buddhist views on abortion):
Of course, abortion, from a Buddhist viewpoint, is an act of killing and is negative, generally speaking. But it depends on the circumstances.
If the unborn child will be retarded or if the birth will create serious problems for the parent, these are cases where there can be an exception. I think abortion should be approved or disapproved according to each circumstance.
In Japan (and Korea per Harvey) it is much, much less restricted and the Japanese Buddhists are much more accepting of it. This was examined in the book Liquid Life: Abortion and Buddhism and Japan. It is notable that both US Buddhists and Japanese Buddhists tend to be much less opposed to abortion than other Buddhist groups.
This issue is explored further in Michael G. Barnhart's Buddhism and the Morality of Abortion, which notes that:
However, as Keown points out, (92) the cases dealt with involve women seeking abortions for questionable, perhaps self-serving, reasons including "concealing extramarital affairs, preventing inheritances, and domestic rivalry between co-wives." In short, if these are the paradigm examples of abortion, then the case is heavily biased against the practice.
In conclusion: We can say that, in general, Buddhism is opposed to abortion and believes that it incurs a significant karmic burden, especially Theravadan and Tibetan practice. Individuals and subgroups, meanwhile, especially in Japan and the United States, fall all along the spectrum with respect to:
- The degree of problem.
- What factors help to balance and to what extent they balance.
- What precisely the state should do about it.
Regardless, the person who has had an abortion should be treated with compassion–not moral judgement–and it should be understood that the decision is pretty much universally a difficult one with a lot of complications and nuances.