I don’t know what was meant by “quasi-Zionist”. There is no Zionism just like there is no communist revolution. It happened: they got their state. There’s a country called Israel, in Eretz Yisroel, that houses about half the world’s Jews.
Whether or not you subscribe to 1930’s Zionism has no impact on bring pro-Israel or pro-Palastinian, other than the forces of bias.
Most Ashkenazy Gedolim took the view that although it may not have been good to start, once it’s here it is a legitimate country. That is how the Steipler says it.
The strength, parameters, and application of the Oaths are very not clear. The repulsion of all Rabbonim to the Zionist groups was because of their supplanting the Torah with Zionism.
Either way, it is a weird obsession to get all upset about a dead cult.