In a surprising and discomforting article for Politico, Darthmouth professor Randall Balmer argues that history is clear: the Religious Right wasn't formed to overturn Roe v. Wade. He writes:
This myth of origins is oft repeated by the movement’s leaders. In his 2005 book, Jerry Falwell, the firebrand fundamentalist preacher, recounts his distress upon reading about the ruling in the Jan. 23, 1973, edition of the Lynchburg News: “I sat there staring at the Roe v. Wade story,” Falwell writes, “growing more and more fearful of the consequences of the Supreme Court’s act and wondering why so few voices had been raised against it.” Evangelicals, he decided, needed to organize.
Some of these anti-Roe crusaders even went so far as to call themselves “new abolitionists,” invoking their antebellum predecessors who had fought to eradicate slavery.
But the abortion myth quickly collapses under historical scrutiny. In fact, it wasn’t until 1979—a full six years after Roe—that evangelical leaders, at the behest of conservative activist Paul Weyrich, seized on abortion not for moral reasons, but as a rallying-cry to deny President Jimmy Carter a second term. Why? Because the anti-abortion crusade was more palatable than the religious right’s real motive: protecting segregated schools. So much for the new abolitionism.
This is "surprising and discomforting" because opposing abortion (whether in some instances or all) can be grounded in religion, particularly the core doctrines that most evangelicals subscribe to. (Quick nit: Balmer does what many incorrectly do—he treats evangelicals and fundamentalists as one and the same. They're not.) Yet, there are no religious arguments for promoting segregation or opposing integration.
However, the historical record doesn't appear as clear as Balmer claims. At least not based on the evidence he presents in his article. Balmer's argument generally is that Americans weren't that riled up about abortion, thus the founders of the Religious Right probably weren't either; instead, they were concerned about busing, but they couldn't galvanize a movement on the platform of segregation so they eventually latched on to abortion.
Unless we assume Bob Jones University to be key to the founding of the Religious Right (and that its segregationist policies were prioritized over the lack of such policies at the college started by Religious Right founder Jerry Falwell), that's a lot of inference without any smoking gun correspondence or statements.