Is there any nationalism which is not on some level chauvinist or which does not have chauvinistic tendencies? It must be so historically unusual, certainly unusual in today's world, as to justify the statement above you query.
Let me be clear (and repeat): I am against Zionism, because I am against nationalism. One reason I am against nationalism is that every nationalism will in the right circumstances develop chauvinist and ethnically exclusivist tendencies.
Of course, as we do for all countries, we should advocate that all citizens of Israel have equality of citizenship, and that the state is institutionally a state of its citizens, not of one ethnic group. Given the composition of Israel's population this is obviously very important, and implies a sort of binational state, Jewish and Arab.
(And of course I am not "equally against" eg Zionism and Palestinian nationalism. But that distinction between oppressor and oppressed nationalisms is surely a different issue from the one we're discussing.)
Let me know where you think we disagree.