As Bradlaugh pointed out below to some extent abortion has become a litmus test which separates the American Left from the Right in the minds of many. Conservative evangelical Christians generally believe that the fundamentals of their faith compel them to support the anti-abortion cause (see this commenter). Historian James T. McGreevy tells another story in Catholicism and American Freedom: A History:
Evangelical Protestants generally ignored the issue until the late 1970s. A group of prominent evangelicals, in fact, cautiously endorsed abortion law reform in 1968, and the Southern Baptist Convention leadership made halting steps in the same direction in the 1970s. When the news service for the Southern Baptist Convention reported the Supreme Court ruling in Roe v. Wade., the first sentence, describing the decision as advancing the cause of “religious liberty,” seemed directed at Catholics arrogant enough to presume that their own views should be law.
Remember that Ronald Reagan signed a bill which loosened abortion laws in California in the late 1960s. George H. W. Bush had supported abortion rights until 1980, and his father had close ties to Planned Parenthood. This is not to say that I deny that those who oppose abortion do so sincerely. Rather, my point is that the “Culture Wars” which we see around us today may seem clear, distinct, and natural, but their shape was far different even a generation back. The flip side of this is that many atheists can not understand how one could be pro-life and atheist, but I would offer that to a great extent this too is an expression of the evolution of a group identity and coalitional politics. There are prominent atheists such as Nat Hentoff & Christopher Hitchens, who oppose abortion rights.
Update: Tom Piatak points out that Hitchens is not pro-life, despite reservations about abortion. The perception that Hitchens is pro-life probably emerges from a column in The Nation where he proposed women given up the right to abortion in exchange to for a cradle-to-grave welfare state.