It's really hard to prove the negative here, as you would need to do an exhaustive search of literally every comment made by right-wing figures in the last 40-50 years to be sure this was never a thing. I will say that I have never heard this specific claim, nor have I read any scholarship making this sort of connection. (For context, I am not a historian--I am a recently graduated lawyer with an interest in the history of American law and courts, especially the partisanship of the Supreme Court). Is it possible? Maybe. But I am skeptical. Republican leaders in the 1970s-onwards would not have felt the need to make such calculations, simply because they were genuinely opposed to both abortion and expanding civil rights, and there were plenty of judicial candidates available who agreed with them. In other words: if you were a Republican opposed to expanding civil rights in the 1970s-onwards, chances are you also were a strong pro-lifer, and you would have chosen judges who were strong on both issues rather than use a judge's pro-life stance as a proxy for his stance against civil rights.

White religious conservatives became a serious force within the Republican Party in the late 1970s and 80s. Before that time, they were not strongly aligned with one party or another. Part of this is due to the fact that the South was essentially a one-party Democratic region for much of the 20th century (the so-called Solid South), and a great proportion of white Protestant religious conservatives lived in the South (especially denominations such as the Southern Baptists). If you were a politically active, white conservative Christian southerner before the 1970s, you were almost certainly a Democrat.

In addition, before the late 1970s, white religious conservatives were not particularly well-organized or galvanized politically--at least, not on a partisan basis. Most scholars point to Roe v. Wade as the turning point, decided in 1973. Religious conservatives were outraged at this decision, as they were by the apparent decline of religious activity in the public sphere (such as the banning of school prayer in 1962). Religious conservative activist groups began popping up and advocating strongly for a variety of Christian-right policies, such as overturning Roe, school prayer, obscenity laws, and more. For example, the "Moral Majority" was founded by Jerry Falwell in 1979; the Family Research Council was founded in 1981; the National Right to Life Committee was incorporated right after Roe was decided; and the Christian Coalition of America was founded in 1987 by Pat Robertson. Most advocacy by these conservatives was directed at the Republican Party, not the Democrats. This was because the Democratic Party had become the party of progressive legislation and civil rights, at least nationally (the situation was more ambiguous at the state and local level in the South, where one-party dominance meant that some rather conservative individuals still ran with a D next to their name).

The 1980 election of Ronald Reagan confirmed the place of white religious conservatives within the Republican Party, when he won 2/3 of the white evangelical vote. Since then, white religious conservatives have been an essential part of the Republican coalition, as we all know.

As time went on, the Republican coalition of voters--overlapping groups of evangelical conservatives, business conservatives, racial conservatives--tended to elevate politicians who believed strongly in all or most of these conservative ideas. Everyone else became marginalized. Hence why you don't see many Republicans who are pro-life and pro-voting rights, or Republicans who are fiscally conservative but pro-choice. These individuals get filtered out of partisan politics--they lose primaries, don't get funding, or don't run at all because they know they'll lose. Take Barry Goldwater. He was the most influential conservative leaders of his generation, running on the Republican ticket in 1964, when religious conservatives were not a strong faction in the GOP. Later in life, he denounced the influence of Pat Robertson and other religious conservatives within the party. A figure like him is almost unimaginable in today's Republican Party. The decline of the so-called Rockefeller Republicans is also telling--these socially moderate, fiscally conservative politicians from the Northeast aren't in the party anymore, in part because religious conservatism is too deeply ingrained in the GOP for them to be viable candidates.

In sum, I don't think it's particularly likely that Republican politicians used pro-life positions as a cover/dog-whistle for anti-civil-rights positions when confirming judges. There would have been no need to. The kind of GOP officials who had power in the post-Reagan era got that power because they embodied the different sorts of conservatism in their coalition--including religious conservatives and racial conservatives. And they chose judges who embodied that conservatism too.