Here's a Roe v. Wade anniversary nugget from Hans Noel's Political Ideologies and Political Parties in America, which shows that the modern-day abortion politics in which people who like tax cuts think abortion should be illegal was constructed from the top down rather than the bottom up.
First here's a chart showing the growing relationship of partisanship and views on abortion, both in Congress and among the mass public:
In part this is a story everyone knows. Before Roe v. Wade, abortion wasn't a partisan issue for elected officials. But the court's actions made it impossible for party leaders to keep abortion off the congressional agenda. Over time, abortion was a large enough element of the agenda that it became incorporated into the partisan agenda—Democrats broadly for more availability of legal abortions and Republicans for less. But rather than the elected officials following the lead of their constituents, it was the other way around. The mass public followed the leader. Over time voters have tended to either conform their views on abortion to those of the party they support or else they switch parties.
This could lead you to the conclusion that the current alignment on abortion is arbitrary. But Noel has interesting evidence that it isn't. Pre-1970 pundits didn't write very much about abortion, but "those who were writing, however, broke down perfectly on ideological lines."
Liberal publications were clearly and forcefully in favor of reforms to abortion laws from at least the early 1960s. The precedent is older: In 1933, the liberal publications The New Republic and The Nation both ran favorable reviews of the pro-legalization book Abortion: Legal or Illegal by A.J. Rongy, a physician. A long piece in The Nation in 1939 claims "the illegal traffic in abortions claims at least 10,000 lives each year" because women often cannot get safe abortions. The piece also treats those who perform abortions as preying on women and profiting from their lack of options. Edwin M. Schur, writing in The Nation in 1955, calls this same problem "The Abortion Racket."
Another lengthy piece in The New Republic in 1963 by James Ridgeway begins, "Reform of the state abortion laws is not a popular cause even though these statutes result in extraordinary inhumanity when they are enforced, and lead to spurious medical practice when disregarded, as they commonly are."
In other words, elected officials didn't "know" that progressive taxation goes with legal abortion until the late-1980s. The public didn't figure it out until the mid-1990s. But magazine writers had it figured out way back in the 1930s!