Origins of Judaism
For centuries, the traditional understanding has been that Judaism came before Christianity and that Christianity separated from Judaism some time after the destruction of the Second Temple in 70 CE. Starting in the latter half of the 20th century, some scholars have begun to argue that the historical picture is quite a bit more complicated than that. In the 1st century, many Jewish sects existed in competition with each other, see Second Temple Judaism. The sects which eventually became Rabbinic Judaism and Early Christianity were but two of these. Some scholars have begun to propose a model which envisions a twin birth of Christianity and Judaism rather than a separation of the former from the latter. For example, Robert Goldenberg (2002) asserts that it is increasingly accepted among scholars that "at the end of the 1st century CE there were not yet two separate religions called "Judaism" and "Christianity"".
Daniel Boyarin (2002) proposes a revised understanding of the interactions between nascent Christianity and nascent Rabbinical Judaism in Late Antiquity which views the two religions as intensely and complexly intertwined throughout this period.
Haskalah
The spreading of Haskalah affected Judaism as a religion because of how much the different sects desired to be integrated, and in turn, integrate their religious traditions. The effects of the Enlightenment were already present in Jewish religious music and opinion on traditionalism versus modernization. Groups of Reform Jews such as the Society of the Friends of Reform and the Association for the Reform of Judaism were formed because they wanted and actively advocated for a change in Jewish tradition, mainly rituals like circumcision. 
Another non-Orthodox group was the Conservative Jews, who emphasized the importance of traditions but viewed with a historical perspective. The Orthodox Jews were actively against these reformers because they viewed changing Jewish tradition was an insult to God and that fulfillment in life could be found in serving God and keeping his commandments. The effect of Haskalah was that it gave a voice to plurality of views, while the orthodoxy stubbornly preserved the tradition, even to the point of insisting on dividing between sects.