It wasn't really a point as much of a process, and one without clear demarcation lines. Progressivism in the late 19 and early 20th century is usually associated with the Republicans, while the truth is, it was more diffuse politically. It is common to point to Nixon's southern strategy as a key turning point in the development of the modern Republican party, but that shift from blue to red in southern states was a 20 year process that didn't really cement in place until the early 90s.

The truth is, until the mid to late 90s, both the Republicans and Democrats were more diffuse in their ideology and had "bigger tents" with real middles. This not only formed the basis for any number of political compromises, but was also a key component of American foreign policy in the Cold War. There are any number of examples on both sides - from the Scoop Jackson wing of the Democrats (whose last members were probably Joe Liberman and Sam Nunn), to the old Northeastern "country club" wing of the Republican party.

The 90s to today have seen both parties solidify toward their extremist wings. There are any number of factors that contributed to this, the most commonly cited being big data's role in gerrymandering and the rise of talk radio and cable news, but neither of those is entirely adequate as an explanation as partisan media and gerymeandering have long histories in America. Political scientists are still coming to terms with things and there is no consensus. Yet, I believe, it is generally understood that the current ideological fights largely emerged in the 60s and 70s (or at least echo them) and these form the underlying basis for the left/right divide of the present situation. The New Left took over the Democrats and the Goldwater Republicans (at least until 2016) took over the Republican party.

It may be better to look at the switch between ideologies as less of a switch and more of a big "sorting" process that began after WWII and ran into the 1990s, before accelerating over the last 20+ years, during which the middle was excluded from the process, (especially in the last 20 years) and certain ideological currents coelesced around the two "poles" of the present two party system.

There are both structural and socio-economic factors involved in this (among other factors) not all of them understood or agreed on, but the "switch" was more of a "solidification" around extant ideologies that were previously not exclusive to either party.

Incidentally, the current Republican party appears to be undergoing a split that echoes the 1850s (know nothing's bear a lot of resemblance to the Trump wing) with the Goldwater/Reagan legacy playing the role of the Whigs, while the Democrats are undergoing their own ideological divide between the older (Clinton) part of the party that is mainly "conservative" in that it seeks to prevent further diminishment of the social/welfare and societal changes it has implemented, and a younger (Bernie/Warren) wing that harkens back to the New Left and it's more radical elements.

There are any number of historians and political scientists that suggest that the current situation is not going to hold and we may be on the cusp of another major shakeup/re-alignment like that of the 19th Century that saw the emergence of the Republican party and death of the Whigs, along with a major shift in the immigrant vote from the pro-slavery Democrats to the abolitionist Republicans, especially in the Midwest German communities.

While that remains a possibility, the previous re-alignment also featured a civil war, so let's hope it goes more peaceful this time if that is the case.