In 1964, the moment when the conservative movement finally gained a significant degree of control over the Republican Party, the GOP convention VOTED DOWN a resolution condemning the John Birch Society. Some have estimated that 10% of folks in the hall were JBS members.
In 1966 Bill Buckley, the godfather of modern conservatism, devoted an episode of Firing Line to making the anti-anti-John Birch Society argument. https://twitter.com/SethCotlar/status/1188317327516790784?s=20
One could plausibly argue that the modern American Conservative movement drew much of its energy from McCarthyite anti-communist conspiracies, and mainstreamed itself by getting liberals to treat such batshit anti-communism as "reasonable" https://twitter.com/SethCotlar/status/1334894318998355970?s=20
At the 1964 GOP convention George Romney (father of Mitt) denounced the Goldwaterite, "Know Nothing extremists" of his day who he feared were taking over the GOP. It was not received well, and such people eventually did take over the party.
Here's a NYTimes article from 1964 that describes the vehemence with which the "anti-John Birch Society" amendment to the GOP platform was voted down. https://movies2.nytimes.com/library/politics/camp/640716convention-gop-ra.html