That's actually not true. Hayseeds and Christian fundamentalists were well represented in the GOP from its founding until the 1930s. It was then that the limosine liberal East Coast set deemed them unworthy of recognition and cast them loose.
Most of the fundies were Democrats, being concentrated in the Democratic South and with no social issues to bother them (with the exception of 1928). Hoover appealed to their simple prejudices, but the New Deal won them over- "limousine liberals" from the East Coast (who weren't "liberal" at all, BTW) had nothing to do with it.
Yes, I was sloppy with calling them 'fundamentalists', who, back then, were snake-handling weirdos. But devout Christians who went to church for two four-hour sermons every Sunday, despised the demon rum, and named their children after Old Testament heroes were absolutely Republican, so long as they lived outside of the deep and upper South.
But you underestimate the effect that the east coast elite sent the GOP hayseeds packing in the 1940s. Between the Wilkie, Dewey, and Eisenhower (who campaigned from NY in 1952) presidential nominations, the conversion of MI Sen. Vandenberg to internationalism, and even Sen. Dirksen's acquiescence to the Great Society, the traditional dry, protestant, small-town conservative had little place in the new party.