Pro-Zionists, Christian Zionists, and others pro-Israel will answer “Yes”. Those who, for various reasons, wish to critique the State of Israel, will respond “No” because they believe that to answer “yes” closes down discussion and criticism of Israel’s actions. My view is that equating Zionism with Judaism is intended to define all such criticism as anti-Semitic. (Despite its claim that it may be legitimate to criticize Israel the Board of Deputies of British Jews rarely, if ever, does: see e.g. http://www.haaretz.com/jewish/news/1.642908 ). None of the above actually answers the question. And we can’t begin to answer until we have an idea of what is meant by those terms.
So, what is Judaism? The answer, “it’s what Jews do” doesn’t help: Jews are as diverse in what they do as is any large group. From non-observant secular Jews, through culturally observant but non-believing to the varieties of orthodox who strive as far as they are able to be Torah observant, Jews are as different, (and as argumentative) as are Christian and Muslim sects. Some of these groups vigorously oppose Zionism: this alone should make us wary of an easy definition. But there are clues…
We can surely agree that Judaism has its roots in the Hebrew scriptures. Second-temple Judaism (4th BC – 1st AD approx.) had a nationalistic-imperialistic hope rooted in their expectation of the coming of the ‘messiah’. In other words, their nationalism depended on a future event. Rabbinic Judaism (mid 2nd century AD – on) held on to the same ‘messianic hope’ but placed this in the framework of diaspora. It was not assimilationist and any nationalism was, for practical purposes, out of sight. In post-enlightenment Europe there developed a ‘cultural Judaism’ – a reasonable, but impossibly broad, category – which tended toward either ghettoization or assimilation. And it was in Northen Europe, where both ghettoization and assimilation were problematic that Zionism grew as a response to persecution and oppression.
The common feature of observant, believing Judaism, whatever forms they take, is ‘hope in the messiah’. Their ‘nationalism’, such as it is, depends on the future event, the coming of messiah. Not only is it ‘Not yet’, since this hope is grounded in scripture, when messiah comes the event will be righteous, reflecting the holiness of God. That does not mean anything goes. God is righteous and therefore will be just. (see e.g. Psalm 82; Mic. 6).
What of Zionism? From its earliest writings it was nationalist and colonialist, and in that sense, imperialist. Being secular it had no hope in a God-ordained messiah, only in its own efforts. Zionisms creators and leaders understood the necessity of, what today we call, ‘ethnic cleansing’. How else could European Jews create a state in Arab populated Ottoman Turkish Palestine? Even the tiny population of Jews were ‘Arab Jews’.
Would Zionists wait for a messiah most did not believe in, even while they attended Synagogue? No, they would be their own messiah with the aid of whatever imperial power they could convince. Herzl tried France, Germany, Turkey with little success. In the context of WW1 Weizmann settled on Britain. Nothing here is ‘messianic’, nothing of Judaism, it is all too human. During its first half-century Zionism was rejected by the majority of world Jewry’s Rabbis. They recognised that Zionism would cause immense damage to Jewry and Judaism. They were not wrong.
So, No, Zionism is not Judaism. The one seeks to honour God and to follow Torah, the other honours power and cares little for God.