Where do you get the idea that most non-religious jews arent halachically jews. Assuminng half the intermarriages have a jewish mother, the person is jewish even if their name is Christian O’Hallahan.
As as I understand it , if someone comes to Chabad and is a zera yisroel, they urge them to convert (Plenty of poskim like Rav Ovadiah Yosef hold this position)