No, this is not even a tiny bit true. What happened is that the mainline denominations are fed from Ivy League seminaries, such as the Presbyterians and Princeton, or the Episcopal Church and Yale, which were completely taken over by leftists in the early 20th century, corrupting those churches and turning them into secular, political organizations.
There were numerous church splits in the 50s and 60s as believers became aware of what was happening in their churches and, being largely unable to take control of the power structure themselves, left and reconstituted. The only mainline exceptions are the Southern Baptist Convention and the Lutheran Church - Missouri Synod. Al Mohler expelled liberals from the SBC seminaries, and Robert Preus expelled liberals from the LCMS seminaries. They weren't 100% successful, but generally changed the direction of those churches.