How Would It Have Evolved

One of the interesting phenomena surrounding the Jewish population of Eastern Europe is how it has taken on an almost mythical status in the minds of so many.  Perhaps it's because of how tragically and quickly the community went from being the centre of the Jewish world into oblivion but our cultural impression of what life was like in the alte heim before the War remains biased towards excerpts from Isaac Bashevis Singer stories of his youth and Fiddler On The Roof.
The true situation, as anyone who is there will tell you, was far more complex.  Jewish life in Eastern Europe ranged from the extreme left to the extreme right.  As Elliot Jager writes:

The striking thesis of On the Eve is that even before Hitler came to power in 1933, the prognosis for European Jewry was bleak: "The demographic trajectory was grim and, with declining fertility, large-scale emigration, increasing outmarriage, and widespread apostasy, foreshadowed extinction. Jewish cultural links were loosening . . . many Jews wanted to escape from what they saw as the prison of their Jewishness."  Millions of Jews abandoned Europe in the interwar period—perhaps 10 percent of the Jewish population; many headed to America. Wasserstein's well-chosen epigraph is from historian Simon Dubnow (whose quixotic championing of an autonomous Diaspora-based Jewish nationalism is itself a historical footnote): "The historian's essential creative act is the resurrection of the dead." 

Wasserstein proves himself to be most adept at the task.  He breathes life into old quarrels, both political and theological: Agudas Yisroel against the Reform; both against the Zionists; the anti-Zionist extremist Hasidim of Satmar against the anti-Zionist fanatics of Munkacz; the General Zionists versus Revisionists, and so on.  Economically, most Jews made their living in commerce or in the professions since anti-Semitic strictures essentially closed academia, government, and agriculture to them. Demographically, by the early 1930s most Jews in Germany were marrying out.

Against all this, Wasserstein's portraits of life in heder, niggun-composing Hasidic rebbes, the workings of yeshivot in Mir, Lublin, and Ponevezh, and a sketch of the Mussar movement show an Orthodoxy in decline but no means defeated.  It faced minor competition from the non-Orthodox whose Budapest rabbinical school, for example, allowed its seminarians to attend (gasp) the cinema. In much of Europe, the real challenge to tradition came from newfound access to the outside world—while in the Soviet Union it was the jealous god Stalin.

It is interesting to wonder what would have happened over time if the Nazis, y"sh, would not have come to power or started World War II.  Alternate histories are generally the realm of fantasy/science fiction writers and are always difficult to discuss with any precision but, as an important secondary character in an excellent fantasy trilogy, I thought I might consider possibilities.
First of all, as the article notes, we have to dispense with the myths.  Not all Jews were religious, some didn't even get a basic cheder education and amongst the religious not all were what we now call Chareidim.  Furthermore, many Jews were not happy about where they lived but remained there simply because they had no place else to go.  By the late 1930's the British, y"sh, had closed the borders to Israel while the Americans, Canadians and western European nations had strongly limited immigration opportunities.  What's more, despite the rising trend to assimilation, cultural exclusion by the main national groups in eastern Europe limited Jewish opportunities in professions and education.  One could be a completely non-identifying Jew with a totally Polish name but that wouldn't help when one came to apply to university or went looking for a job in general society.  How many Jews were Jewish simply because there was nowhere else to go?
Yet things were slowly changing.  Eastern Europe had always lagged the West when it came to societal development, remaining Second World to the West's First World status but over time the nations of the East were progressing.  Emancipation hadn't happened like it did in France and Germany but there was a trend towards liberalization that would eventually have created a more open society if the war hadn't intervened.
As a result one could surmise that other than the Soviet Union, the countries of Eastern Europe would eventually have assimilated their Jews into general culture the way the West did.  Combined with the growing strength of the Haskalah this would have devastated the religious population of Eastern Europe which relied on a great deal of gentile exclusionism and Jew-hatred to maintain the loyalty of the faithful.
All this is idle thinking, of course, but it is fascinating to note one specific quote:"The demographic trajectory was grim and, with declining fertility, large-scale emigration, increasing outmarriage, and widespread apostasy, foreshadowed extinction. Jewish cultural links were loosening . . . many Jews wanted to escape from what they saw as the prison of their Jewishness".
Sounds a lot like North America, doesn't it?