Isn't it just easier to say that 1900s-progressivism and 1960s-progressivism are different but related movements?
The difference isn't any greater than between 2010s Anglicanism and 1950s Anglicanism, I don't often hear this argument related to them. But leaving this aside for now, one movement is quite clearly descended from the other, both in the affiliations of key individuals who connect both down to the chains of cited literature.
First, I'm not familiar enough with Anglicanism to agree or disagree with your assertion. For example, I don't think the statement is accurate about Reform Judaism.
Second, even if current Anglicans take the inside view to assert that they are the same as past Anglican, that doesn't require that we who are taking the outside view must agree with that assessment.
http://unqualified-reservations.blogspot.com/2013/01/noam-chomsky-killed-aaron-swartz.html
Summary: Moldbug on the Aaron Schwartz affair. Power is a very real thing with real consequences for activists, yet many people don't understand the nature of power in modern times. People like Noam Chomsky get great fame doing bad epistomology about who has power, and as a result do great harm to idealistic nerds who don't read between the lines to selectively target their attacks at weak institutions (Exxon, Pentagon) instead of strong ones (State, academica incl. MIT).
Here he returns to a theme that is one of his real contributions to blogospheric political thought: that victory in political competitions provides Bayesian information about who has power and who doesn't. If your worldview has the underdog somehow systematically beating the overdog, your epistemology is simply wrong - in the same way, and to the same extent, as a geocentrist who has to keep adding epicycles to account for anomalous observations.
This means that activists like King, Schwartz, and Assange are only effective in bullying the weak, not standing up to the strong (despite conventional narratives that misassign strengths to institutions). When such activists stop following the script, and naively use the same tactics to attack strong institutions, reality reasserts itself quite forcefully: