No, RR wasn't the catalyst - it was the Civil Rights Act and the subsequent Southern Strategy of Nixon. The Civil Rights Act could not have been passed without Republican liberals in Congress. When LBJ signed the CRA into law, he is supposed to have said, "we have lost the South for a generation" (because until then, the quite-racist South had been a Democratic stronghold - the "Solid South"). When Nixon was running, his campaign manager popularized (though did not originate) the
Southern Strategy:
From now on, the Republicans are never going to get more than 10 to 20 percent of the Negro vote and they don't need any more than that...but Republicans would be shortsighted if they weakened enforcement of the Voting Rights Act. The more Negroes who register as Democrats in the South, the sooner the Negrophobe whites will quit the Democrats and become Republicans. That's where the votes are. Without that prodding from the blacks, the whites will backslide into their old comfortable arrangement with the local Democrats.
The "negrophobe whites" were the key to winning the Southern states, so the GOP had to adopt policies to attract those voters...and that's precisely what the GOP did,
according to Reagan advisor Lee Atwater:
You start out in 1954 by saying, “Ni***r, ni***r, ni***r.” By 1968 you can’t say “ni***r”—that hurts you, backfires. So you say stuff like, uh, forced busing, states’ rights, and all that stuff, and you’re getting so abstract. Now, you’re talking about cutting taxes, and all these things you’re talking about are totally economic things and a byproduct of them is, blacks get hurt worse than whites.… “We want to cut this,” is much more abstract than even the busing thing, uh, and a hell of a lot more abstract than “Ni***r, ni***r.”
This is how the Deep South - which had once been the Democratic "Solid South" - became the electoral base of the Republican party. But that's not all: the Deep South is known by another name, too - the "Bible Belt". An atheist has close to zero chance of getting elected in the South...and because the new base of the GOP is deeply religious, the requirement to be religious became part and parcel of GOP politics. If someone wasn't religious or - horrors! - was against things like prayer in school or posting the Ten Commandments in the courtroom, well, obviously that someone wasn't a conservative, and therefore wasn't a Real American.
And as the GOP became the party of the Religious Right, opposition to all things liberal became not a matter of politics...but a matter of religious conviction.
That is how the GOP came to hate liberals. Reagan wasn't the catalyst - even Bob Dole says that Reagan, Bush 41, or himself would have a "very hard time" getting elected in today's GOP. Reagan was just one part of a truly tectonic sociopolitical shift.