People can be broadly generalized as right-wing or left-wing on any particular political issue. (Obviously.) Among the religious Jews whom we would identify as right-wing, it seems to me that their political and religious beliefs come about in two very distinct ways.
First, there are people whose primary motivation is religious, and due to certain Jewish commandments or attitudes have come to reject "land for peace" and other more left-wing political approaches. Unfortunately, these people are hard to conclusively identify as being in this category, since deep questions of "what came first, politics or religion" cannot be answered based on a few superficial observations.
The best example I can think of in this category is R' Yaakov Medan. The depth of his involvement in social, judicial, and educational issues, his innovation and enthusiasm when engaging in a broad range of religious scholarship, and (I posit from personal experience) the way he interacts with people, are all out of character for someone whose driving motivations are nationalistic. And yet there should be no questioning his right-wing-ness: I'm fully convinced that he regrets not expelling the West Bank Arabs in 1967, and would likely be willing to do the same today.
However, R' Medan is unusual in that the scope of his accomplishments allows us to carefully evaluate what he does and does not value. For normal people like us who make only a limited contribution to the public domain, it is very difficult for others to know what really motivates us.
The people on my second category are much easier to identify. They are those whose religion is simply an appendage of their nationalism. They often don't make a substantial time and effort commitment to learning Torah or engaging in chessed activities. The males among them don't always even go to minyan! But if you ask them to name the person who they most respect and who best exemplifies their worldview, they will invariably point you to a rabbi (generally named Kahane). In a certain sense, therefore, their religiousness is quite deep. But their deep allegiance makes a peculiar contrast with the lack of enthusiasm they show in acting on the more trying of their beliefs.
How does such a combination come about? The answer is simple. Aware that contemporary moral expectations do not allow for wars of conquest or killing Arabs, these people find in certain Jewish sources an alternative basis for their jingoism. A little honesty requires that they adopt the whole of Jewish practice in order to feel justified in believing in what they see as Jewish attitudes. But rarely do they show the same enthusiasm for these "derived" beliefs that they do for mouthing off about the latest comments by an Israeli government minister.
Now, you will tell me that most of the religious right-wing Jews you know fit neither of my stereotypical descriptions. They are neither entirely focused on the Torah to the exclusion of political attitudes not found in the sources, nor is their Judaism a crutch used solely to legitimize their political views. My hypothesis is that rather than fitting neither category, they fit both. Their are motivated by purely religious and purely political beliefs, to greater and lesser extents depending on the person. These motivations, while of separate origin, are mutually reinforcing to a certain extent and generally they live in happy coexistence.
But in their roots, one of these motivations is pure and the other impure, and religious Jews would do well to remove the latter from their consciousness. The prophet Amos tells us that God does not do special favors for the Jews any more that for the Ethiopians, Philistines or Arameans. Our privileges over the Arabs in Israel are limited to the extend of our observance of the Torah. If like secular Zionists a century ago we lose sight of that fact, then we will end up losing not only the Torah, but also our rights in the land and eventually our very will and ability to continue living there.