Here are a couple examples of initially neutral or moderate organizations that became left wing bastions:
Academy of Motion Picture Arts and Sciences
Screen Actors Guild–American Federation of Television and Radio Artists
Writers Guild of America
Directors Guild of America
National Education Association
American Federation of Teachers
American Psychological Association
American Sociological Association
Modern Language Association
American Historical Association
Association of American Universities
Columbia University
Harvard University
Yale University
University of California, Berkeley
Oberlin College
Reed College
NPR
PBS
The New York Times
The Washington Post
The Guardian
Human Rights Campaign
GLAAD
Good luck finding examples of the opposite direction.
The New York Times and The Washington Post left wing bastions?
Either your list is way out of date or the Overton Window is so far to the right in the US that this statement is somehow possible.
There are many more institutions on that list that are explicitly not left wing by non-US standards.
Here are a few examples of initially neutral or moderate organisations that are harboring enemies of His Majesty Homer Simpson:
Academy of Motion Picture Arts and Sciences
Screen Actors Guild–American Federation of Television and Radio Artists
Writers Guild of America
Directors Guild of America
National Education Association
American Federation of Teachers
American Psychological Association
American Sociological Association
Modern Language Association
American Historical Association
Association of American Universities
Columbia University
Harvard University
Yale University
University of California, Berkeley
Oberlin College
Reed College
NPR
PBS
The New York Times
The Washington Post
The Guardian
Human Rights Campaign
GLAAD