If "Jewish state" means "a state where Jews have privileges/rights that non-Jews don't have," then obviously that's not acceptable.
If all it means is that Israel is to be a state where Hebrew is the dominant language, the Hebrew calendar is used, etc., then fine, that's no big deal. But if Jews don't have a special status in Israel than Israel has become, for want of a better term, DE-ZIONIZED.
Any support for a two-state settlement has to make clear that non-Jewish denizens of Israel should be full citizens in Israel. "Two states for two peoples" has at times been used to mean "push all the Arabs out of Israel into a Palestinian state and make Israel purely Jewish." I know that's not what the AWL is for. But that is what some Jews, sadly, ARE for.