Marx was part of the Young Hegelians. Marx and Engles were part of the Communist League (if not it's literal sun around whom the League revolved), and Marx and Engels were also the founders of the German Workers' Society.
The idea that Marx was a recluse internet style poster with no attachment to real society is a 21st century invention to make vaguely left people feel better about their alienation and a strawman for the right to attack.
Rutgers and Princeton have an intertwined history, but that's pretty much it. Rutgers is seen as a good state school and to many it's mostly because it sounds like a private school.