Hmm, I think that the USA has probably shifted rightward since the 1970s/1980s.
While "cosmopolitan" positions on same-sex marriage, reproduction rights and race are all en vogue right now, there's a building neol-liberal corporatism in both major parties. Opposition to trade restrictions, increases in the minimum wage and truly progressive taxation is much more prevalent now than it was 40 or 30 years ago.
This, 100%. America is not shifting leftward in any meaningful sense. It has become a more educated, urbanized, cosmopolitan country, and the culture has shifted to reflect this, but America, like 90% of the world, has been hurdling rightward and neoliberalizing on basic economic issues for decades, with no real end in sight.
This can be completely flipped around. What social conservatives see as "shifting leftward" is, as you say, simply society progressing into the 21st Century and certain ideas/customs becoming less accepted. Well, the United States economy and the businesses/industries that allow it to thrive benefit more from neoliberalism and free trade each decade, and we're simply adapting. That doesn't, to me, constitute a "shift rightward." By the 1980s, Republicans had called out Democrats for wanting to pretty much "tax and spend," and the American people bought it. Democrats have yet to really win them back over, though I guess Bernie is taking a big step forward.