Sorry no. The only study that ties abortion rates to party uses "number of women that have ever had an abortion. It does not measure repeated abortions.
Some data points at the difference:
Abortion rates by state: Pre- and post-Dobbs data show substantially higher rates (abortions per 1,000 women of reproductive age) in states that lean Democratic and have broader access (e.g., New York, Illinois, New Mexico) than in more restrictive or Republican-leaning states. One New York Times analysis of CDC data noted that roughly 68% of abortions occurred in states that voted for Biden in 2020.
Repeat-abortion rates tend to be higher in states with higher overall abortion rates, simply because a larger share of women become eligible for a subsequent procedure. Again, this is not broken out by individual party ID.
So the data leans towards dems getting abortions more often per woman, where republican women who have had at least 1 abortion is close to the number of democrat women that have had 1 or more abortions.
Most women are liberal when they are young, but then reality hits and they turn conservative. Perfect example is Shoeonhead.