R. Nathan Lopes Cardozo offers a solution to the "conversion crisis", in which many Gentiles in Israel consider themselves Jews but are not willing or able to halakhically convert (link):
The answer, we suggest, is the “two brotherly people solution”: Jewish Jews and non-Jewish Jews. This would involve creating communities of “non-Jewish Jews” in which those who are not prepared to go the whole way could develop their own brand of Judaism. They could have their own synagogues in which to practice aspects of Jewish tradition that they wish to use. They could decide for themselves to what extent to observe Shabbath or keep kosher. Their wedding ceremonies could make use of many Jewish rituals and they could have their own “Jewish” cemeteries where they could adopt as many Jewish religious practices as possible rather than be forced to bury their dead in totally secular or non-Jewish burial grounds. We could set up outreach programs for them, enabling them to study Judaism and choose whatever aspects they wish to adopt. We could even create yeshivoth and seminars for this specific purpose.This seems to me to be a recipe for schismatic disaster, not to mention the encouragement of intermarriage by those who will see this all as a technicality.
Perhaps it depends on one's judgment regarding whether the result will be better or worse than the current intermarriage situation. I have insufficient knowledge with which to form an opinion. However, the creation of "Non-Jewish Judaism" scares the bejabbers out of me.