To be serious about this, obviously you can. Abortion's contemporary alignment on the liberal-conservative axis was by no means inevitable. Prescott Bush, who was attacked in his early 1950's campaigns as a supporter of Planned Parenthood in Connecticut, I doubt had many particularly liberal instincts, in keeping with his background. I'd even argue that there would be conservative--though somewhat "ugly"--reasons for backing abortion: maintenance of stable populations and stable nuclear households, a crime and poverty-reduction measure, ensuring that the "surplus population" doesn't get too out of hand, and so on. One need not even use the tired "limited government" pleas in order to make this case. How many times do you hear random white kids joke about African-American families' perceived overabundance of children and tie it to reliance on welfare? This type of conservatism could have been especially prevalent if the GOP stuck to a "managerial" path. Population politics, which played at least some part of each president's policy from Johnson to Carter, seem to have utterly disappeared after 1980. Conversely, Jill Stein's comments on abortion might seem more mainstream in this world.
I haven't gone through and combed fifty-year-old policy statements to confirm or deny this, but I've been told that between, say, the sixties and the nineties, you see Ted Kennedy and Bob Dole 'evolving' on abortion in diametrically opposed directions.