Can you clarify your definition of "Zionism"?

It seems to be widely defined as the establishment and maintenance of an explicitly Jewish state.

That is correct, but Jewish in this context is an ethnic group, not a religion. Much of the original Zionist movement was comprised of secular Jews.

"Explicitly jewish" could be a democratic state with jewish majority. And it could be a jewish minority ruling over a non jewish majority.

Most Israel want the former. A hard core minority wants the latter. The last few decades the latter set the tone because the dovish side of the map hadn't propose a viable course of action to change the status quo. The moderate majority is too scared and it lost faith in trying to reach a peace agreement again after the violence the last try brought, And the "death to israel" rhetoric of palestinian leaders.

So while the majority is pretty moderate, the perceived lack of partner basically put in power an extreme right minority. This might change as there's an undercurrent of population change, where the new majority might be less preoccupied with western values of democracy and citizen rights.

You are technically right, although currently it's a mixed bag. Many cite religious as the reason for not letting go of the land, others simple Zionism.

As for letting go of the entire country, there is nowhere else to go, as for giving the Palestinians what they want, just look at the trouble Gaza alone is causing, look how many innocent civilians (on both sides, mind) Hamas has killed. I don't think for the majority of Israelis it's ideological.

You're conceptually right, but the current right wing in Israel is very much centered around the concept of a united Israel rooted in Biblical reasoning.

Zionism might not be religious, but the political forces that would prevent relinquishing territories in modern day Israel very much are.