Earlier quoted context omitted.
> This is cultural Marxism. No, it's actually Marxism losing relevance in favor of something radically different, but in any case it's fairly irrelevant to the Democratic Party which never generally adopted a ”New Left” position, following classical moderate, non-Marxist pro-labor focus into the 80s, then abandoning that and anything like the Left generally for the center-right neoliberalism of Clinton's “Third Way”.
Bill Clinton was a centrist, and that's part of why I think he was so popular as president. I had not considered what you say as a possibility. I always thought the Marxists were the real power in the Democratic party and they implemented their policies slowly and incrementally. Does neoliberalism really hold sway in the Democratic party and what I considered incremental marxism was really just left-of-center Clinton…
The most powerful faction in the Democratic Party are center-right neoliberals like the Clintons, the next most powerful are center-left Social Democrats (including what passes in the US, but not really by international standards, for “Democratic Socialists”.) There are essentially no Marxists in influential roles in the Party. There's probably a few Marxists (or Leninists/Stalinist/Maoists) in the electorate that hold their nose and vote for Democrats as, from their perspective, the very slightly lesser of two evils (and probably some who vote for Republicans as the greater evil in hopes of provoking revolution), but they aren't really driving the party, either by having their hands on levers of power or being an actively courted constituency.
> Does neoliberalism really hold sway in the Democratic party and what I considered incremental marxism was really just left-of-center Clintonian politics?
The first, yes, the second...well, insofar as it is not Marxist, sure.
> How does the constant ratcheting up of identity politics stuff fit in to your theory, though?
While there are Left forms of identity politics, other-than-proletarian-identity politics are not Marxist even when they are somewhere on the Left, though the practitioners (even among right-wing identity politics) may draw something from Marxist (or Leninist) tactics or analytical modes (Marx's adaptation of Hegelian dialectic is widely influential in this way), but this doesn't make the movements involved politically Marxist.
And while the Democratic Party does include some who pursue Left forms of identity politics, it predominantly pursued bourgeois feminism and the similar bourgeois versions of other group-rights movements, rather than any of the Left (for instance, radical, socialist, or Marxist) versions.
While to anti-feminists (etc.) the distinction may seem irrelevant, it's actually quite critical to leftists of all stripes.
Bourgeois identity politics (and the fairly overt rejection of Left identity politics) is a fairly key part of Clintonian Third Wayism.