moan about centrists and moderates until the second coming of Lenin or whatever
It has everything to do with power dynamics. The American centrists and moderates maintain the limit of allowed mainstream political discourse as there is no distinction between a liberal and leftist. In fact every attempt is made to maintain them as synonyms.
In America centrists and moderates define themselves as leftist, and they view anything further left of themselves to be something like unchecked authoritarianism.
Thusly the American right-wing gets to successfully operate from the default position of linking leftism to authoritarianism in all discourse and debate.
So most of the American Left is just plain stuck trying to escape this paradigm because the basic terms don't have the same coherency.
Not that the distinction bears much value making: They funded the proto-Nazis.
In the time period in question (After WW1, Wiemar Germany) the social democrats were in direct coalition with right wing paramilitaries.
Those paramilitaries did some extrajudicial killings and some just so happened to form things like the S.A. and the Nazi party. (And tried to overthrow the social democrats government a number of times by military coup.) Erich Ludendorff is a notable figure to this period.
But by the time the proto-Nazis had murdered themselves and others enough to become the Nazis, no, the social democrats were no longer in alliance, but mostly after the second coup attempt.