Judaism
There are some movements that combine elements of Judaism with those of other religions. The most well-known of these is Messianic Judaism, a religious movement, which arose in the 1960s, that incorporates elements of Judaism with the tenets of Christianity. The movement generally states that Jesus is the Jewish Messiah, that he is one of the Three Divine Persons, and that salvation is only achieved through acceptance of Jesus as one's savior. Some members of the movement argue that Messianic Judaism is a sect of Judaism. Jewish organizations of every denomination reject this, stating that Messianic Judaism is a Christian sect, because it teaches creeds which are identical to those of Pauline Christianity.
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.