The situation was mostly middle-ground, but the US in Cold war? In the USSR, the far left policies gave way for the Far right stalinists to take charge when Lennon died.
The problems with the USSR were a case of leftists making mistakes that allowed reactionaries to take over, not a case of conservatives being on the right side of history.
It wasn't really a switch, more like both parties having an ideological shift. A switch implies they didn't change core beliefs at all and just flipped, when many of the beliefs of both parties changed.
The parties never switched. The Democrats just started pandering to the minorities they've been fighting against the entire time because they were losing a lot of votes.
Republicans freed the slaves. Republicans ended segregation.
Democrats just keep promising change that never comes.
Look, I'm pretty centrist and do my best to split my vote for both parties if policies align, but you can't ignore or handwave away the southern strategy. Republicans have been pandering to conservatives for decades.
Besides, many of their policies have been implemented. The change you say hasn't occured definitely has, just mostly at state levels. Obamacare is still pretty successful.
The federal government has barely done shit in ages.