Rahm Emanuel is part of the left wing here and the left wing in Israel. Many do not understand that the animosity between observant/traditional Jews and the Liberal Left Jews is a powerful one. This animosity, which includes the rejection of the Torah, is at the core of what drives people like Rahm Emanuel. A bibical comparison might be the’Erev Rav’, or even the insurrectionist of the bibical figure Korach.
The Erev Rav only followed Moses into the desert because they desired to be close to the real power. Somewhat like those who come to America to bilk it for its resources.
Korach asked what was so special about Moses when he saw himself as every bit a leader. So he demanded power from Moses and convinced a significant number to follow. Moses could do little about it until God himself destroyed Korach and all his followers.
Combine all of this with R.E’s Israeli nature of ‘in your face’ and you can get a fairly good idea of Rahm Emanuel.
To say that the Jewish political world divides along those lines is obviously just a generalization with many exceptions. I, for one, would not classify myself as an observant Jew, yet I have always detested the left for its threat to civil liberties and the rule of law wherever it gains control of a society and its threat to the very survival of the great twentieth century achievement of the state of Israel. You could call me a Jewish secular conservative/libertarian/Zionist.
On the other hand, there also those Jews who are traditional/observant, yet still cling to the dogma of the left. In particular, Rahm Emanuel himself reportedly belonged to and may still belong to an Orthodox congregation. How can you fit him into your dichotomy?