A very significant portion (very possibly a majority) of non-Orthodox “Jews” (secular, Reform, Conservative) that self-identify as Jewish, are in fact non-Jewish. These Goyim who are members of the Reform or Conservative movements, or these gentiles who identify themselves as “Jewish”, descend from — or are themselves — invalid conversions from the Reform and Conservatives.
Or the false conversions in Israel of Russians and Ethiopians who never were religious, never intended to be religious and never kept one Shabbos.
Or alternatively were deemed “Jewish” by virtue of patrilineal descent (mainly in the Reform and Reconstructive movements, but even the Conservatives accept their so-called Jewish status, as they cross-recognize the other movements), having a Jewish father and a Gentile mother. Or being several generations down from said goy (great-grandmother) or were adopted by non-Orthodox Jews, or descended any number of generations back from such a child.