Isn't there already a profound schism in Judaism? I remember being in a reform synagogue where a member was semi-jokingly ridiculed for having a frum child- "I don't know where he went wrong".
Then there's the built-in sentiment of Orthodox that non-orthodox/Chassidishe/Haredi Jews are almost-non Jewish because they do not observe mitzvos, and even many people accepted by Reform or Conservative movements as Jews (e.g. Reform converts or those with a Jewish father but not mother) are not accepted as Jewish by the Orthodox.
Still, throughout the history of the Jewish people, it has been mitzvos and Torah that have maintained the Nation, not ethnic identity. In the beginning there was no ethnic identity- Avraham Avinu circumsized everyone in his household, including his slaves. Later people who were ethnically Jewish converted to Xtianity to escape persecution, and all along the way people who were not ethnically Jewish converted to Judaism.
The turning point in this I think was the Shoah- for the first time people were persecuted on the basis of ethnic identity regardless of religious practice rather than just being forced to convert to something. Now we live in a time when our psyches are so shaped by this event that ethnic Judaism really means something because we fear it might mean something to someone else. And many people are embarrassed by religious Jews- perhaps because the nation's psyche still sees them as dangerously obvious, and being associated with that kind of obvious Judaism as a risk of persecution. Whether or not people can come to a Jewish practice or agree with the Orthodox philosophy/halakha/lifestyle seems irrelevant here.
People from any country or nation do not seek to be separated from their compatriots ethnically because of a religious difference- they differentiate themselves religiously, even politically and this is enough. An African Christian and and African Moslem do not seek to remove their African-ness because they feel it is "tarnished" by people practicing different religions. There have always been and likely will be religious strife, but the link of an ethnic identity and a religion is really unprecedented and new. To a certain extent, it is even false- the "ethnic" life of Sefardi and Askenazi Jews is hugely different. The two are considered Jewish by virtue of having ancestors who practiced the Jewish Religion, not by virtue of having a particular gene set (which is usually the determining factor in an ethnicity).

My great fear of the Jewish people having this kind of schism is because of where I think it comes from. As much violence as Hitler has done to our Nation, our ethnicity, and our history, that event continues to work on us today when we try to separate from one another to prevent too much Jewishness from ruining everything.