Many of the early jewish socialists regarded socialism with religious zeal. I looked for a quote online and found this attributed to Berl Katznelson, an early founder of labor zionism – “Everywhere the Jewish labourer goes, the divine presence goes with him.” I don’t know what language he said it in. It sounds like he’s quoting Rav Kook.
I would question the assumption in the original question that socialism caused them to go otd. It’s entirely possible that many were leaving anyway. Religion and socialism are not mutually exclusive. Many Eastern European Jews who immigrated to America left religion behind and never became socialists.