Here's my two cents on the right-ward slide of the Western states. By Western, I refer to the states highlighted in the map below in orange, and to a lesser extent the ones in yellow, which overlaps with the Midwest.
FDR, of course, swept every state but Pennsylvania, Maine, and Vermont in 1932, and won all but Maine and Vermont in 1936. By 1940 and 1944, the Western states became voting more Republican, but for the most part Roosevelt had success in the West. A part of this is the somewhat forgotten aspect of the New Deal that was the electrification of the United States. Through infrastructure spending, millions of Americans who never had easy access to electricity suddenly did, and this, coupled with the expansion of dams, other resource-based employment opportunities, and Secretary of Agriculture Henry Wallace's development of the 'Ever-Normal Granary' dramatically increased job opportunity and standard of living in the West. However, the West
was typically more inclined to conservatism due to their rural nature, and also tended to favour international isolationism, and so more often voted for moderate Republicans such as Willkie and Dewey. New Dealism made a comeback in 1948 under Truman in the West less-so because of a regained appreciation of large-scale government spending projects and socially progressive causes (such as Truman beginning to desegregate the military) and more-so because of Truman's staunch anti-communist positioning that was popular in the formerly isolationist states pre-disposed to conservative lifestyle and fear of totalitarian socialism. Dewey's complete and utter lack of campaign substance in 1948 didn't hurt either.
As for the Eisenhower years, I believe that Republican success had more to do with Eisenhower himself being such a popular and recognized figure rather than it being a complete turn against the Democrats. With the economy recovering, the West would have likely voted more conservative with a financially comfortable 'status quo' back, but if a more typically Republican had been nominated - especially Robert Taft - they would have done well in the West but lost nationally. By 1960, the West had more fully settled into conservative-leaning economic and social positions that had more to do with ruralism and the 'frontiersman' mentality then it had to do with entrenched racism. While I'm not saying that the American West was some sort of equal rights egalitarian utopia during the 1960s, due to the very small number of racial minorities in the West, I suspect Westerners just didn't care all that much about it segregation either way, which made it an open field for political figures such as Mike Mansfield of Montana to take pro-civil rights stances without fear of major backlash at home while in other parts of the West, 'folksy conservative' types such as Roman Hruska remained popular while still voting for civil rights legislation. That's why, in my mind, Johnson won in the West in 1964 by painting Goldwater as too radically conservative, but why the West voted overwhelmingly for Nixon in 1968 and 1972 because of a 'law and order' campaign that appealed both to segregationists as a race-baiting dog-whistle, and to more apathetic Westerns who believed law and order was what the country needed after headlines filled with riots and assassinations in the dens of sin that was urban America.
And from then on, I think that mentality stuck in the West of the 'law and order,' 'family values' brand of country conservatism that lasted through Gerald Ford and Jimmy Carter and was emboldened by Ronald Reagan's election and the rightward drag of the Overton Window that came with it. While some Western states have become more reliably progressive, or at least moderate, due to population growth and urbanization, as well as demographics changes that favour the Democrats (e.g. New Mexico, Nevada, Colorado) the 'traditional West' has arguably shifted from moderate conservative to reactionary 'paleoconservative' stances that were harnessed by Bush Jr, the Tea Party Movement, and most recently, Donald Trump. While the War on Terror has certainly added a xenophobic angle to Western conservatism, I think it remains, at its core, about fiscal conservatism and a resurgence of the economic and international non-interventionism that originally held sway there. Who knows, maybe the West will vote Democrat once the economic crashes again, which is looking to be sooner rather than later.
tl;dr The rise of Western conservatism in the 1960s and beyond was a result of resurgent rural attitudes of small government mixed with growing religious evangelism, and the mentality created by Nixon of the great importance of 'law and order' for Americans.