I'll attempt to answer this question from a US perspective only, although similar realignments may be occurring globally. Basically the parties are both undergoing ideological shifts which are significant in my view, the Progressives are casting off their Hegelian roots, and Conservatives are departing from Buckley, Burke and Locke traditions. Incidentally, both have opted for deeply anti-intellectual (maybe post-intellectual?) ideologies in their places.
The Democrats are struggling with three contradictory, non-supportive ideological focal points, two of which represent divergences of progressivism, one of which is very recent.
As a point of departure, the Progressive movement started in the very early part of the 20th Century, but had it's intellectual roots in Hegel, Focault, and Marx (Marxism is to some extent watered down Hegelism). James Ceasar put it thusly:
The party was the carrier of the great progressive tradition that stretched back from LBJ and JFK to FDR and ultimately to the progressive intellectuals John Dewey, Herbert Croly, and Charles Beard. These thinkers introduced the transforming idea of "social intelligence," a concept that demanded the continuous application of rational government planning, under the aegis of social science, to the ills of the modern industrial age. Social intelligence was intended to direct and accelerate the forward course of history. The conviction that progress was certain, so long as social intelligence was deployed, was the premise underlying the entire project.
This way of thinking was largely intact in the 1960s, when hundreds of social scientists took leave from their universities to make the great trek to Washington to serve their nation and party.
You can also find the Hegelian traditions alive and well, for example, in the jurisprudence of Supreme Court Justice Breyer
GEORG HEGEL was a German philosopher of the early 19th century. Hegel believed that history unfolds through a "dialectical" process, in which each stage is the product of the contradictions inherent in the ideas that defined the preceding one. Within these tensions and contradictions, Hegel believed, the philosopher can discern a comprehensive, evolving, rational unity. He called that unity "the absolute idea." History consists of an inevitable and progressive march to that idea.
Until recently it appeared that Marxism (which borrowed Hegel's dialectic but replaced "ideas" with economic systems and classes--hence "dialectical materialism") would represent Hegel's most enduring contribution to the modern world. But then Communism collapsed. Now it can be argued that Hegel's most enduring contribution is found in American constitutional law.
How did the metaphysical speculation of a 19th century German historicist, whose teachings were congenial to Marxists but are anathema to modern analytic and positivist philosophers--as well as proponents of the Constitution as originally understood--come to influence our constitutional law? The answer lies in the concept of the "living constitution"--and in the influence of Woodrow Wilson.
This flavor of Progressivism is still rhetorically alive today, as some of Barack Obama's and Bill Clinton's locutions, such as the "arc of history" attest. But as an animating and intellectual force it is largely spent. Consider Jonathan Gruber's role in passing Obamacare, a Progressive program cut from the same mold of those in the 1960s. In the Progressive tradition, the benefits of the program would have been debated forthwith and "social scientists" of that movement would have considered Gruber's assertion that the ACA was passed only because of the stupidity of the American voter to be something of an anathema.
Enter the rise of the New Left
James Ceasar (ed note, a professor of mine) does an excellent job of describing the New Left's ascendency and what they stood for:
For those in the party's mainstream, the revolt of the New Left and the "counterculture" came as an enormous shock. It was as if their own offspring had suddenly and unnaturally turned on their progenitors and set about mercilessly to devour them. The New Left called into question almost everything liberals had deemed to be progress: material well-being, American power, and especially the enlightened motives of the leaders of the American nation. Liberalism was part of the problem, not the solution. In the words of the movement's political manifesto, the Port Huron Statement, "What we had originally seen as the American Golden Age was actually the decline of an era." The moral disaster over which liberalism had presided, culminating in the Vietnam war, was so fundamental, so interwoven into the fabric of American life, that only a revolution could save us. The New Left married a deep pessimism about America to an unbounded optimism about the transforming power of revolution.
Those who look at the writings of the New Left today will find very little if anything that stands the test of time. None of the movement's intellectual luminaries, from Norman O. Brown to Tom Hayden to Charles Reich, can be counted a substantial thinker. Nevertheless, many leaders of the movement engaged in concerted argument--indeed, felt obliged in their political action to expose the theoretical problems of the liberal tradition and to advance their own ideas. Thought mattered to them. Their arguments evidently had an impact, too, as many liberal intellectuals succumbed before the theoretical onslaught. It turned out there was no theoretical position the liberals believed was true. The "best and the brightest" proved lacking in conviction, while the radicals were full of passionate intensity.
This split between the liberals and the radicals in the late 1960s and early 1970s cost the Democratic party its confidence, and the party has never been quite the same since. The New Left did not take over permanently, a task for which it was morally, intellectually, and above all politically unfit. Once it became clear--as it did in the 1972 election--that the majority of the American people had no sympathy for the New Left's cause, especially "revolution," the old liberal mainstream was in effect asked to step back in and serve as the public face of the party, and it did so in the persons of Walter Mondale and Michael Dukakis.
But the New Left didn't disappear. Renamed the cultural (or multicultural) left, it decamped from center stage and repaired to safer quarters in the universities, where it managed to carry out much of its program. Inside the Democratic party, it ceded actual leadership, but maintained an impressive power base and exercised enormous influence on the policy agenda. Usually, the old liberals found the cultural left too dangerous to embrace, but too powerful to resist.
The Democrat party has see-sawed ideologically from the failures of Progressivism evident in the failures of Vietnam, and the Great Society (and Communism generally) and the anti-intellectualism of counter culture, protest wing of the Democrats.
This position has been forcefully argued by some party intellectuals, most recently Michael Tomasky in a lead article in the American Prospect. "What the Democrats still don't have," Tomasky wrote, "is a philosophy, a big idea that unites their proposals and converts them from a hodgepodge of narrow and specific fixes into a vision for society." Even more disturbing to Tomasky, however, is that the party has lost the capacity to engage in this kind of thinking; its spirit is now anti-intellectual. "The party and the constellation of interests around it," he writes, "don't even think in philosophical terms and haven't for quite some time."
The Cultural Left or New Left finds it footing in Intersectionality
Intersectionality is defined by Wikipedia as
Intersectionality: Intersectionality (or intersectionalism) is the study of intersections between forms or systems of oppression, domination or discrimination. An example is black feminism, which argues that the experience of being a black woman cannot be understood in terms of being black, and of being a woman, considered independently, but must include the interactions, which frequently reinforce each other.
From Damon Linker Links in the original to several excellent source materials.
In the fierce post-election debate about how Democrats should respond to the party's astonishing electoral collapse at all levels of government, some have argued that identity politics is the problem, while many others (especially younger activists) have claimed it's the solution.
Those inclined toward the latter position would be well advised to read a recent New York Times story very closely. An account of growing rancor surrounding the planned Women's March on Washington (scheduled for the day after Donald Trump's inauguration), the piece demonstrates with admirable clarity how doubling down on identity politics — and especially the left's embrace of the trendy postmodern ideology of "intersectionality" — is likely to shatter the Democratic Party into squabbling factions even more vulnerable to a resurgent right.
I think it would be hard to debate that the ideology of intersectionality and identity politics is not the primary animating force among the Democrats today, and it's precisely that ideology that had ramifications in the most recent election.
Linker goes on:
It would be one thing if Democrats had reason to hope or expect that they would be saved by demographics. Ever since the "emerging Democratic majority" thesis was first floated more than a decade ago, leading liberals have been convinced that their side is bound to prevail as the country becomes less white over time and minority groups eventually combine to form a left-leaning electoral majority. In such a situation, a politics based on racial, ethnic, gender, and other forms of identity might make sense as a mobilization strategy.
The focus on identity politics and social justice does not appear to receding among the Democratic faithful and is being coupled and alloyed with socialism and progressive economic strains.
As the founding of the Republican party was dedicated upon the re-application of neo-liberal thinking of the Founders, especially the ideas embedded in the Declaration of Independence, the revival of GOP force as an intellectual movement in the 50s and 60s had those same ideas and moralities reapplied. Center to this move were Goldwater, as Brythan, states in another answer to this question. Also deeply involved were William F. Buckley, Hans Morgenthau (and his intellectual heir and collaborator Kenneth Thompson, also a professor of mine), Reinhold Niebuhr, the Chicago School of Economics, headed by Milton Friedman (and his heir Thomas Sowell), and the Austria economic leaders headed by Hayek. So the above thinkers represent most of the best of the ideological basis of the modern Republican movement until the present day, and it too serves as a point of departure.
Enter Brain Dead Conservatism* coined in the first article below
The first to notice an ideological shift in the party, way back in 2009, was Steven Hayward in a Washington Post Article and it presaged the coming of Trump.
During the glory days of the conservative movement, from its ascent in the 1960s and ’70s to its success in Ronald Reagan’s era, there was a balance between the intellectuals, such as Buckley and Milton Friedman, and the activists, such as Phyllis Schlafly and Paul Weyrich, the leader of the New Right. The conservative political movement, for all its infighting, has always drawn deeply from the conservative intellectual movement, and this mix of populism and elitism troubled neither side.
Today, however, the conservative movement has been thrown off balance, with the populists dominating and the intellectuals retreating and struggling to come up with new ideas. The leading conservative figures of our time are now drawn from mass media, from talk radio and cable news. We’ve traded in Buckley for Beck, Kristol for Coulter, and conservatism has been reduced to sound bites.
This populism is just reactionary in the sense that it waits to get punched, and then punches back. The chip on their shoulders is evident. Hayward points to many other examples in his well referenced article.
Other examples of this phenomena that Hayward doesn't point out include:
Matthew Continetti, in Commentary:
Lately, though, it’s seemed as if the process by which William F. Buckley legitimized American conservatism has gone into reverse. . . As conservative media has proliferated, the authority of any one man or publication or radio show or television network has receded to the point of invisibility. For a time conservatism may have resembled the Catholic Church, with Buckley as pope, issuing bulls and ex-communicating heretics. But conservatism these days more closely resembles Islam, with untold numbers of mullahs issuing contradictory fatwas, with antagonistic schools of thought competing for adherents, with not a few radicals eager and willing to blow the whole thing up.
And Tevi Troy, in Politico
One of the most spectacular fissures of this already dramatic political season has been the messy, public divorce of the Republican intelligentsia from the party’s suddenly energized populist voter base. . .
It’s easy to lay the blame at Donald Trump’s feet (after all, it’s hard to imagine another Republican candidate of the last four decades rejecting National Review so cavalierly), but this year’s split between intellectuals and the rank-and-file GOP goes beyond the front-runner. In fact, neither of Trump’s remaining rivals, Ted Cruz nor John Kasich, is particularly cozy with the conservative intelligentsia. . . What’s really going on is that the ideas that the conservative intellectual community has been peddling for decades have failed to appeal to an angry blue-collar voter base. What worked in Reagan’s era just doesn’t work anymore, and Trump is simply exploiting the divide.
Whether or not this populist strain in conservatism is here to stay, or what will occur in the conservative party post-Trump is hard to say. One of the schisms in the party, the international adventurism of neo-conservatism that advocates nation building appears to be suffering considerably.