Historically, political party identification and abortion views have often been correlated, but not in a way that Americans younger than 40 would recognize.
The first Protestant denominations to make a push in a pro-choice direction were also the most Republican at the time: Presbyterian and Episcopal. The Catholics and Southern Baptists, both strongly Democratic constituencies at that time, remained stauchly opposed to abortion. The Black Panther Party opposed birth control through the early 1970s, so one can only speculate their views on abortion. Jesse Jackson was pro-life at least until 1977, the year he wrote a position paper for the National Right to Life Committee.
Closer to (my) home, here in MI the (initially unsuccessful) push to legalize abortion in the early 1970s was led by Protestant Republicans in the state legislature; the largely Catholic Democratic legislators were opposed. An unsuccessful 1972 initiative in MI to legalize abortion through 20 weeks received just 40% of the vote in heavily Democratic Wayne County-- and 51% in (then) heavily Republican Oakland County. The 1978 gubernatorial elections in both MA and MI featured a pro-life Democrat against a pro-choice Republican.
Nationally, the transition took place in the 1970s; I believe 1976 is the first year the party platforms took the positions on abortion (Dems pro-choice; GOP pro-life) that characterize the parties today.
So, the answer to your initial question is: No.