In my relatively short life, I've identified with a huge variety of Israeli political parties (in rough chronological order): Meretz, Likud, Labor, Shinui, and Kadima (the current ruling, centrist party). Shinui, which translates to "change", was at the time roughly between the center-left Labor and the center-right Likud, which appealed to me for at least two reasons: my already demonstrated indecision with regards to Israeli politics, and my then ascendant courtship with centrism. Moreover, Shinui's focus was not on security issues but on another matter of Israeli affairs which is very important to me: religious discrimination (particularly, but not exclusively, against less-observant Jews. Such as myself.). Specifically, it campaigned vigorously against the institutionalization of Orthodox Judaism as the sole acceptable form of Judaism in Israel, and generally for a more secular, universalist state.
Though at one point it was the third largest party in Israel, Shinui is now basically defunct (Kadima occupied its centrist niche), but it's mission continues to be important. I do think that Israel ought to remain a Jewish state, but that Judaism must be tempered by a respect for the human rights and equality of all citizens: including women, including gays and lesbians, and including people of all religious backgrounds. The effort by the ultra-Orthodox to turn Israel into a theocratic state is incredibly dangerous from the standpoint of the global Jewish community, for it both undermines Israel's moral legitimacy and threatens Israel's role as a haven for all Jews, not just the preferred castes of them.
American Jews have, from the beginning, been important in envisioning and enacting the path by which Israel will travel. It is critically important that we maintain that mission and take every step we can to check the growing power of Israel's own religious right.
Oh, and for the record: Attempting to segregate and subordinate women is the exact opposite of Rosa Parks' legacy. Just to clarify.