How could you arrive at a Presidential election where Ronald Reagan is running for President against Jimmy Carter...but the former is a Democrat while the latter is a Republican?
With an early enough POD, keeping Reagan as a Democrat is relatively easy given he was a New Deal liberal who campaigned for Truman and Hubert Humphrey in 1948. Given his charisma, Reagan could still very well go into politics but become known as a staunch advocate of labor liberalism while being criticized as a typical left-wing divorced Hollywood actor by the right.
Making Jimmy Carter a Republican is somewhat more difficult but still doable given that Jimmy Carter's 1970 gubernatorial run was to the right of the incumbent(and involved some racial dogwhistles) and he was a protege of Lester Maddox. I don't think its impossible for him to follow the path of other Southern Democrats like John Connolly or Strom Thurmond in becoming a Republican, especially given his evangelical beliefs.
What would the dynamics of such a reversed election look like? Who would be the most plausible running mates in this case?