This changed, according to the podcast, because of a segregationist named Paul Weyrich, who “understood that racism -
I have confirmed that Weyrich was a segregationist who did see abortion as this galvanizing issue where segregation wasn’t
I have not found confirmation of this.
Weyrich set up the Heritage Foundation, which does not appear to be segregationist, nor does Weyrich.
The point I can derive is as follows:
https://www.politico.com/magazine/story/2014/05/religious-right-real-origins-107133/
For nearly two decades, Weyrich, by his own account, had been trying out different issues, hoping one might pique evangelical interest: pornography, prayer in schools, the proposed Equal Rights Amendment to the Constitution, even abortion
Secondly, in 1976 Bob Jones University had its tax exemption rescinded, due to its segregationist policies.
Thirdly, in 1978 anti-abortion Senators won both Senate seats in Minnesota.
According to the Politico story following the 1978 victory, evangelicals begun campaigning against abortion, touring the country.
In earlier years, opposition to abortion had been a Catholic issue, and evangelicals were much less concerned, however with the huge rise in abortions following Roe v Wade

then things had changed, and abortion became a political issue.
The argument that Weyrich was concerned with segregation doesn't appear. What does appear, is that Bob Jones Jr, Jerry Falwell, et al, ran segregated Christian schools, and they were unhappy at the government moving against them, and this led them to try to seek political support for their segregated schools, so they became a Republican bloc, whereas at that point young white evangelicals were more likely to support the Democrats.

In 1982 Reagan planned to support Bob Jones University in its argument for segregation, however an outcry meant they did not do so.
So in summary from what I can see:
- no, abortion was not primarily a substitute for segregation, in that it is clear that abortion became an issue because of campaigning by Christians who had nothing to do with segregation, such as Francis Schaeffer.
- abortion was an issue in its own right, given the recent legalization and large rise in abortion
- segregationist Christian pastors did seek to ally with the Republicans politically in order to continue segregating, and they got help from the Republicans on this matter
- it appears that Weyrich did portrary Carter and the Democrats as anti-Christian, and sought to portray Carter as to blame for IRS moves against segregated Christian schools, and hence to mobilize evangelicals towards the Republicans
- this further intensified when Carter refused to pass a constitutional amendment against abortion (https://amc.sas.upenn.edu/sites/default/files/Balmer%20-%20Historian%27s%20Pickaxe.pdf)
Therefore we essentially have two separate issues being used for political ends by a Republican strategist:
- abortion, which became a bigger issue after it was legal and common
- segregation, in that he said to the segregationist pastors - we will help you if you support us
It doesn't seem credible to argue that abortion was a substitute for segregation, because this starts from the initial assumption by the questioner, which is not sourced, that Weyrich was motivated by segregation/racism, as opposed to Weyrich being a political strategist motivated by political power.
The idea that there was some sort of 'abortion as a proxy for segregation' implies a sort of political process that doesn't really exist. Conservativism reacts to contemporary issues, and in a culture war may seek to talk about them constantly, and can use them to gain political power (talking about LGBT, etc.), but for example Weyrich's Heritage Foundation was setup with a standard conservative goal of 'lower taxation'. The idea of the pro-life movement being a giant conspiracy on behalf of segregation is not credible, even if this movement did involve many people who had initially coalesced in support of segregation - the fact that there was at that point already a political coalition of Southern segregationist pastors because of IRS action against their schools meant that they were easier to mobilize against subsequent issues. It strikes me that there is an intended ad hominem here that 'they didn't really care about abortion and just wanted to be racist'.