I think the above posts have probably explained most of the reason for this—the socially liberal or progressive attitudes of most American Buddhists, and the lack of a decisive doctrine within Buddhism (more on this below)—but there is another factor at work here. And that is that the Dhamma is not a legalistic morality. The fact that something is wrong doesn’t mean that it should be illegal. No-one in Buddhism, to my knowledge, is arguing that spraying cockroaches should be made a crime, or that alcohol be banned, even though these things are obviously against the precepts. And I think there are good reasons for this.
State intervention can’t be justified simply on account of something that I (or my community) find morally wrong. Another necessary condition is that the intervention should actually be effective in reducing suffering. And in this regard, I think it is reasonable to be pro-choice, even if you think abortion is unethical as a matter of personal morality.
The social reality is that making abortion illegal does not reduce the number of abortions: it just makes them harder, more dangerous, and more expensive. The best way to reduce the number of abortions is not by criminalizing women’s choices, but through education, contraception, and support for women’s health and autonomy. There are consistently fewer abortions in regions where such sane policies prevail.
To briefly remark on the relevant Buddhist doctrines, a number of things need to be borne in mind. First up, knowledge of the process of conception, and in particular, being able to test whether one is pregnant, are much more advanced now than in the Buddha’s day.
The passage most often cited in this context is from MN 38 Mahatanhasankhaya Sutta, where conception is said to require three things: the mother is fertile, the parents come together, and the gandhabba (consciousness to be reborn) is present. What is usually overlooked is that, according to the suttas, this is not a Buddhist doctrine at all, but a brahmanical one. In MN 93 Assalāyana it is explicitly ascribed to a group of brahmin ascetics. There’s nothing unusual about this: plenty of stuff in the suttas is derived from the brahmins. But it does caution us to avoid over-interpreting this single passage. The purpose of the passage is not to define the first moment of life, but to show the various conditions that are required for conception.
The Vinaya defines abortion as taking life, and monastics are forbidden from recommending it. But this must also be understood in the context of Vinaya. Stealing is likewise forbidden, “even as much as a blade of grass”. The point is that monastic ethics are intended to keep monastics away from even the slightest transgression, and are not meant to provide a template for a legal compulsion.