Summary: Religious Jews were mostly indifferent to the Zionist movement before the founding of the state of Israel. For the sake of not angering the gentile countries of Europe, many were opposed to the Zionists who they viewed represented disloyalty to the countries. After the founding of the state, and the non-dominance of the non-religious, the religious Jews became mostly pro-zionist with some caveats.
Before the fall of the Ottomans
Religiously, the "return to Zion" was always seen as a positive thing but it was practically extremely difficult. The majority of Jews in Europe lived in the Russian Empire and were extremely poor and could not afford to risk abandoning their meagre, but stable, existance on a pipe dream. Most who attempted to find a better life spent that chance on going to America, but there was organized settlement of Palestine by very religious European Jews beginning in the 1800s. It was sponsored by philanthropists such as Moshe Montifore and the Rothschilds. At that time, the Ottoman Empire was far away from falling and an independent Jewish state was not on the radar for these early settlers. Almost all religious Jews were, in theory, in favor of moving to Palestine and it was easy to have these views because in practice not much would come out of them.
Around the time of and after the fall of the Ottomans
After the Ottoman Empire was dismantled, being in favor of an independent Jewish state carried weight, because it was a real possibility and not an empty aspiration. The majority of religious Jews became more opposed to moving to Palestine because 1) It could be seen as disloyalty by the European countries in which they lived 2) The majority of Jews involved in the Zionist movement were non or even anti-religious.
Most of the European Jews were killed or displaced by the Holocaust. For those that survived, consideration #1 was no longer relevant because the Jews came to the realization that their loyalty to their countries did them no good. Religious European Jews split up between America and Israel.
There was a concern that the non-religious Jews in Israel would try to undermine the religious lifestyle. A deal was made early on whereby various guarantees were given to the religious community (eg. control over who counts as a Jew, control over Jewish weddings, military exemption for seminary students). The vast majority of religious Jews are now in favor of Zionism but some who live there dislike the elements of "Israeli" culture that differ from those of traditional Judaism.
A few small groups are opposed to any return to Zion that does not involve the Messiah.