You would have to define Leftist.
Conservatives and Republicans until recent decades were not Jewish friendly.
Jews, like most, have a tendency to gravitate to where they feel comfortable. And for a long time that was the Democrat party.
NY, the most Jewish of States, had long term Republican Senators and Governors, because those individuals earned the trust of the Jewish community.
That Tikkun Olam crap is a very recent explanation. Jews moved Left because that is where they found emancipation from ingrained anti Semitism.
Jewish tradition- as can be seen by those who keep Jewish tradition, the Orthodox- is very Conservative.
I define leftism as socialist, or those philosophies derived from or based on it.
I certainly agree that Jews moved left as a reaction to antisemitism. I think this happened in Europe, well before the great immigration here of c. 100 years ago. I also think that "conservative" antisemitism has been responsible for keeping American Jews on the left up through WWII. Perhaps the current persistent leftist antisemitism and leftist anti Israel attitude will change this. Not so much the Orthodox Jews, I think.
As far as I know, not being much of a scholar, or very religious, you are right that traditional Jewish teaching, in the sense to which you have referred, has nothing to do with leftism, as it far predates it. I hadn't meant to say that leftism was part of Judaism, merely that European and American (and probably European?) Jews of the last 120 or so years have more often than not adopted leftist political beliefs.