fornias

After the 2016 election, Nate Cohn grouped together 13 states under the term 'Appalachafornia'. He called them 'Trump's base states' and noted that Trump won them collectively by the same raw vote margin whereby Hillary Clinton won California. However, it's not clear just how he chose these 13 states. They are not Trump's top 13 states by vote share--he got higher vote shares in non-Appalachafornia Missouri (56.77%), Indiana (56.82%), Mississippi (57.94%), and Louisiana (58.09%) than he did in Appalachafornia states Kansas (56.65%) and Montana (56.17%).  

However, the one thing that all the 'Appalachafornia' states--and only the 'Appalachafornia' states--do have in common is that they gave Trump a > 20% margin over Hillary Clinton.

On the presumption that Nate Cohn's criterion for including a state as part of 'Appalachafornia' in 2016 was that Trump won it by at least 20%, we can enumerate 'fornias' for every nominee. (I will take the liberty of also adding as a criterion that the nominee received at least 55.5% of the vote in the state; Trump's lowest vote share in 2016 in any of his 'Appalachafornia' states was 56.17%, in Montana. There are cases, even in two-party elections, where a nominee wins a state by over 20% but without reaching or even approaching a landslide vote share [a case in point being Louisiana in 1960], in which case it seems unfitting to call it a 'base state' for that nominee. The CQ Almanac has used 55% as a threshold for indicating states a nominee has won particularly strongly, for example, in its recap of the 1976 election: 'Six of the 10 states in which Carter received more than 55 per cent of the vote were in the South...')

Each map is coloured in with each party's fornia for that year.

2020.
2016.
2012.
2008.
2004. (Aside from the 'fluke' of Indiana [which has returned to giving Republican nominees > 55.5% in both 2016 and 2020], none of George W. Bush's fornia states in either of his elections has ever gone on to vote Democratic to date, which is not true of his father's fornia states in 1988.)
2000. (Compared to the last several close elections--1976, 1968, 1960, even 1948--2000 was unusual in that one nominee had such an expansive fornia. Gore's carrying the second-largest electoral prize [and still the second-most-vote-casting state] by over 20% in a close election was also relatively unprecedented, although Kerry was unable to reprise this in 2004.)
1996. (This was the last time one of the two major nominees had no fornia, at least by my definition; Bob Dole won Utah by 21.07%, but his vote share in Utah was 54.37%.)
1992. (The highest vote share either nominee got in any state was Bill Clinton's 53.21% in Arkansas, and no state gave any nominee a > 20% margin in any case.)
1988. (One can see a somewhat broken version of the Republican 'L' here, although none of the Southern states in Bush Sr's '88 fornia went on to be part of any subsequent Republican fornia.)
1984.
1980.
1976.
1972. (In landslides, the lighter-shaded states are ones that fulfil the criteria to be part of the winning nominee's fornia, but either gave him a lower vote share than the nation overall, or voted for him by a smaller margin than the nation overall. In both 1972 and 1984, the Republican 'L' is on full display.)
1968.
1964.
1960.
1956.
1952.
1948.
1944. (The last time, outside landslide conditions, in which the Democratic fornia included an interior Mountain West state.)
1940. (This year, the Democratic fornia included multiple Mountain West states.)
1936.
1932.
1928.
1924.
1920. (Eleven of Harding's fornia states had voted for Wilson in 1916, all but New Hampshire west of Beatson's Line. Meanwhile, three Hughes states [Delaware, West Virginia, and Indiana] did not become 'fornia' states for Harding.)
1916. (Wilson's fornia also included multiple Mountain West states.)
1912.
1908.
1904.
1900. (Even in 1900, Bryan's fornia included one Mountain West state, Nevada.)
1896.
1892.
1888.
1884.
1880.
1876.
1872.
1868.

These are the lowest vote shares received by the nominees in the last several elections, and some other select (two-party) elections, in any of their 'fornia' states:

2020
Biden: Connecticut (59.27%)
Trump: Utah (58.13%)

2016
Trump: Montana (56.17%)
Hillary Clinton: Vermont (56.68%)

(In Vermont, Bernie Sanders got 5.68% of the vote as an unsoliciting write-in candidate; Montana was Gary Johnson's fifth-best state, giving him 5.64%.)

2012
Obama: California (60.24%)
Romney: Tennessee (59.48%)

2008
Obama: Connecticut (60.59%)
McCain: Alaska (59.42%)

2004
Bush: Montana (59.07%)
Kerry: Vermont (58.94%)

2000
Bush: Kansas (58.04%)
Gore: Massachusetts (59.80%)

1976
Carter: Arkansas (64.94%)
Ford: Alaska (57.90%)

(Eugene McCarthy, the principal 'other' candidate nationally, appears not to even have been on the ballot in Alaska; but it was by far Libertarian nominee Roger MacBride's best state, with 5.49% [his second-best showing was 1.35%, in Hawaii].)

1972
Nixon: Montana (57.93%)
McGovern: n/a

(Montana was John Schmitz's sixth-best state; he got 4.23% in it.) 

1960
Kennedy: Massachusetts (60.22%)
Nixon: Kansas (60.45%)

(In this election, which was very two-party even by the standards of two-party elections, all of both nominees' 'fornia' states were states that gave them over 60% of the vote, as seems fitting for an exceptionally two-party election. However, in what appears to be the instance of the lowest vote share whereby a nominee has carried a state that gave him a > 20% margin in a nationally two-party election, Kennedy got a > 20% margin out of Louisiana despite getting only 50.42% of its vote. 20.99% of Louisiana's vote went to unpledged Democratic electors.)

1936
Franklin Roosevelt: Ohio (57.99%)
Landon: n/a

(Ohio was William Lemke's seventh-best state; he got 4.39% in it.)

1932
Franklin Roosevelt: Washington (57.46%)
Hoover: n/a

(Norman Thomas got 2.78% in Washington, somewhat above his national 2.23% finish; more strikingly, Washington had by far the greatest proportion of vote for nominees other than Hoover, Roosevelt, and Thomas, at 5.83% [followed by 2.79% in Idaho]. William Hope Harvey of the Liberty Party received 4.93% of Washington's vote; he polled 0.13% nationally, in sixth place.)

1920
Harding: Washington (55.96%)
Cox: Texas (59.34%)

(Washington was Farmer-Labor nominee Parley Christensen's best state, giving him 19.37% of the vote; other than Washington, only South Dakota, which gave Christensen 19.04%, gave him above 7%, making the two states relatively idiosyncratic. Christensen polled 0.99% nationally.)

1916
Wilson: Arizona (57.17%)
Hughes: Vermont (62.43%)

(Arizona was Socialist nominee Allan Benson's seventh-best state, giving him 5.47%.)

1908
Taft: Oregon (56.39%)
Bryan: Arkansas (57.31%)

(Taft also got a > 20% margin out of California, where he got 55.46% of the vote--just below the 55.5% threshold [and above the 55% threshold that had been determined as 'official' in defining a 'landslide' by the 1980s]; and Bryan also got a > 20% margin out of Georgia, where he got a 54.60% vote share. Eugene Debs got 7.41% in California and 6.62% in Oregon, and Thomas Watson got 12.59% in Georgia, by far his best state. No one third-party candidate did spectacularly well in Arkansas; Debs got 3.85%, and Thomas Watson and Eugene Chafin [Prohibition] each did better than a third of 1%.)

1904
Theodore Roosevelt: Nevada (56.66%)
Parker: North Carolina (59.71%)

(TR also got a > 20% margin out of Montana, where he got a 54.21% vote share. Nevada was Eugene Debs' fourth-best state, giving him 7.64%, and Thomas Watson's sixth-best, giving him 2.84%. Montana was Debs' second-best state, giving him 8.81%, and Watson's eighth-best, giving him 2.36%.)

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The lowest vote shares that have translated into a > 20% margin have been pluralities, and have taken place in elections in which the national two-party vote was below 94%:

Delaware, 1860 (Breckinridge, 45.54%)
Massachusetts, 1832 (Clay, 47.27%)
New York, 1848 (Taylor, 47.94%)
Louisiana, 1968 (Wallace, 48.32%)
Kentucky, 1912 (Wilson, 48.48%)
Maryland, 1912 (Wilson, 48.57%)

Kennedy (barely) cleared a majority in Louisiana in 1960 (and Winfield Scott likewise barely cleared a majority in Vermont in 1852).

As of now, the most recently that a nominee has gotten a > 20% margin without clearing 55.5% was the three-way contest of 1996, when Bill Clinton did so with a 51.62% vote share in Maine and a 53.35% vote share in Vermont, and Bob Dole, with a 54.37% vote share in Utah.