As far as Republican presidents or prez candidates being mostly moderate past and present, people have to remember that until about fifty years ago, most politicians on the national stage were social conservatives. The current Dem Party presidents and prez candidates didn't start their "progressive" i.e. leftist bent until George McGovern was nominated in 1972. Even FDR, who created the welfare state, didn't have a social program as radical as McGovern's. He was even too radical for me a Dem at the time. I voted for some candidate down the list neither Nixon nor McGovern. No, not Wallace.
So, many of the hot social topics of today like abortion and homosexual marriage were never big issues until around 1970. The great majority of people from both parties before 1970, pols and non-pols, agreed on most social issues. Like my Dem-voting parents who were about as socially conservative as you could get.
Goldwater was the first Republican presidential candidate who outlined a conservative vision for America. Reagan was the first elected Pubbie prez who tried to put a conservative program into practice. Coolidge was pretty conservative, but he never stressed a conservative program like Goldwater and Reagan did. Eisenhower, Nixon, and the Bushes were all more moderate.
Will the Pubbie prez candidates after Trump be conservative, moderate, or populist? Who knows?