Can a party be leftist and Zionist?
No, it cannot. But the concept of leftist Zionism is still being pushed to cover up its racist, colonial nature.

Ahead of Israel’s October 27 elections, Israel’s Young Democrats, the youth wing of the newly formed Democrats party, are seeking foreign allies. They recently announced a joint campaign with the Young Greens of Austria to support “progressive voices on the ground and work with them towards a sustainable peace”.
Meanwhile, another youth group described as “leftist”, Hamahanot Haolim (the Ascending Camps), is exploring plans to build a new kibbutz in the occupied West Bank, near Jericho.
When questioned about the impact on the Palestinian population, the group’s director, Ilan Gazit, explained that since Israeli settlements are being built regardless, “the left” should make sure it is Israeli “leftists”, not far-right settlers, who populate them. “We aren’t ashamed of this, and we aren’t hiding it,” he said.
Mapai was established as a Labour Zionist party in 1930, led by David Ben-Gurion. It became the dominant force within early Zionist politics and the principal architect of the pre‑state and early institutions, including the Haganah, which carried out various terrorist attacks and massacres against the Palestinians.