Surely those who practice Judaism support Zionism?
Not true. I come from this background and I can tell you: Most hardline orthodox jews believe they have NO BUSINESS being in the land of Israel, because the vast majority of israel's population is atheist/secular and is living in open sin and disobedience to the Torah.
The jews who tend to be most pro-zionist are the reform/conservative/ and some non-haredi orthodox jews.
The hardline orthodox jews teach and believe that in order to inherit the land, Torah obedience is a must.
As for what you said about the temple, there is disagreement among the rabbis. There is a saying we have: Put two rabbis in a debate and you come up with three answers.
There is a group which teaches that the MESSIAH will come and build the temple. Some teach that we got to build it now, and then the Messiah will simply show up there.