Do you remember the last time a far right Republican won the Presidency?
One who was to the right BEFORE or AFTER the election?
This is where the so-called labels cause problems. Ronald Reagan did NOT govern California in anything resembling an "extreme" manner. We can argue the "why" (mostly the Democrats controlling the legislature for good portions of his tenure - don't recall the specifics as he was really governor before my time) but Reagan was by no means an extremist governor. Ford successfully painted him as one in the 1976 NH primary when Reagan proposed $90 billion in savings that would have caused NH to have to raise taxes (that's the one state up there you just don't do that) and it probably cost Reagan the nomination.
But you see I've been told for years about the President Reagan who cut taxes on the rich and raised them on the poor and ran up a huge budget deficit and nearly destroyed the country with his venture into right-wing fanaticism. Now - all these years later - I'm being told by the same ideologues (no reflection on seebell here) about the courageous Reagan who raised taxes unlike the modern Republicans and blah blah blah. In point of fact, Reagan's actual governance was NOT extreme - but he was regarded as the most ideological President since Hoover (at the time of his election) by no less than political centrist writer Teddy White. It is anachronistic to go back now and say Reagan was NOT viewed as extreme when he was elected. Indeed, the fear at the time was that his big talk was going to cause WW3.
If we're going to use that standard then even Goldwater cannot be considered an extremist. In fact, Barry even jokingly told Bob Dole that they were "the new liberals of the Republican Party."
If you use the standard of the time, Goldwater WAS an extremist. In 1976, Carter was actually viewed as more conservative on most issues than Ford was. In both 1980 and 1984, it was left vs right and Reagan won. Same with 1988 but to a lesser degree. In 1992, both candidates were seen as centrist (and Clinton DID run as a centrist - name me any Democrat seeking the Presidency in that six election run that proposed revamping welfare, advocated the death penalty, and proposed CUTTING taxes on the middle class) but only one was to blame for the election.
So seebell - at the risk of sounding like Clinton here (the definition of "far right") - if you go by perception at the time, Reagan certainly qualified. If you go by actual governance then it was probably Hoover. Fact is that both parties label the other and yet in almost every case they nominate candidates of the center.