There are definitely forms of Zionism that claim relationships with Marxism, anarchism, and other Left traditions. These movements have always had challenges from other Left movements among Jews (not to mention Palestinians, Arab communities, and the anti-imperialist Left in general).
An academic example looking at Zionism and its relationship to racism: The company Gale (that makes a variety of online and print reference sources) recently included an entry on Zionism in their Encyclopedia on Race and Racism. Pressure/input from Zionist groups have led them to make alterations to the entry.
The entry can be viewed here.
[This is a PDF file and may take some time to load on your computer]
Within U.S. Jewish communities, there is a history of rejecting Zionism as a liberation movement. One book to read on this topic is:
Prophets outcast : a century of dissident Jewish writing about Zionism and Israel / edited by Adam Shatz. New York : Nation Books, c2004.
A current Jewish group (that I work with, to be transparent) called the International Jewish anti-Zionist Network (IJAN) has the view that any form of Zionism must be rejected as an ideology and practice if one believes in social justice (from an anti-imperialist and anti-racist framework) for all people. The group’s charter is here.
Currently within Israel there is the Anarchists Against the Wall formation, and the Shministim, both which are critical of Israeli policy but don't make a clear stance against Zionism.
From a Zionist perspective: The Zionism and Israel Information Center has a list of their own definitions.
And from Mideast Web comes their history of labor Zionism.
There is a recent article on Labor Zionism that is available online and is described in this way by its authors:
“We have written an article that examines the contradictions at labor Zionism's core, with a combination of historical analysis and first-person reportage. "'Bring on the bulldozers and let's plant trees': The Story of Labour Zionism" shows how the movement has used the longing for social justice to bolster Israel's oppressive system. This critique is especially timely given the Israeli Labor Party's central role in the most recent campaign of atrocities against the Palestinian people of Gaza and elsewhere. The article appears in the current issue of the Canadian-based radical journal Upping the Anti (# 7, October 2008).”
Inside Israel in the 1960's and 1970’s there was a group called Matzpen, which considered itself socialist and anti-Zionist. A collection of their articles can be found here.
Further back: Inside Russia’s Pale of Settlement, starting in the 1890’s, the Jewish and socialist Bund movement rejected Zionism as a movement that would guarantee justice for Jews. They were part of the general movement for socialism for all in Russia, but organized as Jews to guarantee Jewish cultural autonomy and civil rights.
Some works on the Bund are:
[Book] The Jewish Bund in Russia from its origins to 1905 [by] Henry J. Tobias. Tobias, Henry Jack. Stanford, Calif. : Stanford University Press, 1972.
[Book] The politics of futility; the General Jewish Workers Bund of Poland, 1917-1943, by Bernard K. Johnpo Johnpoll, Bernard K. Ithaca, N.Y. : Cornell University Press, [1967]
[Article] Arkady Kremer, Vladimir Medem, and the Ideology of the Jewish "Bund" ; Koppel S. Pinson; Jewish Social Studies, Vol. 7, No. 3 (Jul., 1945), pp. 233-264 ; Published by: Indiana University Press
