In some cases yes, and in some cases no. Zionism's a very diverse set of ideologies, so there's no quick answer.

For some Zionists, the main priority of Zionism was essentially to get Jews somewhere safe from prejudice, discrimination, or violence. This was the sort of Zionism Herzl championed--he was inspired in large part by the trial of Dreyfuss, a Jewish soldier in the French army who was wrongfully convicted of treason due in large part to antisemitic prejudice against him, a story which Herzl covered as a journalist. Herzl's writings imagine a Jewish state which is essentially just like regular non-Jewish Europe, idealized for what Herzl believes and likes. It's essentially Germany with better labor rights, but also a safe place for Jews.

But Herzl's school of thought wasn't really the only one. Ahad Ha'am, for instance, saw a Jewish state as a way of revitalizing Jewish society and culture, the idea being sort-of parallel to other national revival movements in Europe. This doesn't really have much to do with antisemitism.

There are others that are sort of implicitly a response to antisemitism, but aren't as explicit as Herzl's. Revisionist Zionism, whose main early proponent was Jabotinsky, saw Zionism as part of rejecting what he saw as Jews being weak in exile. Which points to his rejection of acceptance of Jewish life under discrimination or persecution, which is about antisemitism without being a direct response to it.

As for which Jews favored or rejected it, Zionists tended to be a subset of secular Jewish political movements, of which there were many who disagreed with Zionism. Traditionalist Jews weren't Zionist, but neither were Reformers who identified more with non-Jewish national movements--early Reform Judaism rejected Zionism for quite a while. Communists weren't Zionists. Bundists (a Eastern European Jewish political ideology that believed in Jewish autonomy and was socialist) weren't Zionists. But after WW2, most of those political movements were ecclipsed. The aftershocks of the Holocaust made Reformers change their tune. Bundists in Europe were essentially all dead, and never became a significant political movement in the US. Zionism and Orthodox Judaism remained somewhat complicated, but the upshot is that while there were lots of competing Jewish political philosophies early on, eventually Zionism sorta trumped all of them.