I posted this soon after Barack Obama was re-elected President. Electoral votes shown are for 2008.
When all is said and done, I think that the Obama and Eisenhower Presidencies are going to look like good analogues. Both Presidents are chilly rationalists. Both are practically scandal-free administrations. Both started with a troublesome war that both found their way out of. Neither did much to 'grow' the strength of their Parties in either House of Congress. To compare ISIS to Fidel Castro is completely unfair to Fidel Castro, a gentleman by contrast to ISIS.
The definitive moderate Republican may have been Dwight Eisenhower, and I have heard plenty of Democrats praise the Eisenhower Presidency. He went along with Supreme Court rulings that outlawed segregationist practices, stayed clear of the McCarthy bandwagon, and let McCarthy implode.
gray -- did not vote in 1952 or 1956
white -- Eisenhower twice, Obama twice
deep blue -- Republican all four elections
light blue -- Republican all but 2012 (I assume that greater Omaha went for Ike twice)
light green -- Eisenhower once, Stevenson once, Obama never
dark green -- Stevenson twice, Obama never
pink -- Stevenson twice, Obama once
No state voted Democratic all four times, so no state is in deep red.
Electoral votes are for a time now passed and can be ignored.
Some President must be most like Obama in political skills and temperament... and regional appeals. Obama is not a perfect match for Ike, as Obama did not win in farm-and-ranch country in the Rocky Mountain States and the High Plains as did Eisenhower. Political cultures rarely change starkly over sixty years or so in states (although demographics and economic bases can). Many Obama supporters considered Ike the last really-good Republican President. This said, I can much more easily connect Eisenhower in behavior to Obama than to Trump. I can't speak for Ike, but I think he would find Obama an expression of most of what is best in America and Trump a disgrace.
The Parties can change when the political culture does not.Can you imagine any Republican winning Massachusetts, Minnesota, and Rhode Island together... twice? Republicans have had only five wins of those states altogether by Presidential nominees since 1960. Ike must have been doing something right to win those three states... twice! His six wins in those three states in two elections is more than all Republican nominees from Nixon to Trump. Four of those come from near-sweeps of the USA.
Eisenhower and Obama did very well among the well-educated. Both did poorly in the South, except, oddly, they were the first to win Virginia in a long time (24 years for Ike, 44 years for Obama) for their Parties. Coincidence? Aside from Virginia not being easy pickings for a populist I see nothing obvious.
The most obvious cross-Party comparisons involve the winners winning 45 or more states, so of course Nixon 1972 and Reagan 1984 are obvious comparisons to FDR in 1936. This said, when someone wins 325 electoral votes that the nominee of the other Party won twice and the other seven come from places not voting for President in the previous time, then there must be some marked similarities.
Obviously, Colorado, Nevada, and New Mexico are very different from what they were in the 1950's.