Monotheism leads to intolerance. Instead of travellers asking “what gods rule here?” and politely fitting in and leaving their own religion at home, or merging cultures swapping and combining gods like old friends, “oh, you have a god/prayer just for stubbed toes? I'll remember that!”, you have now a culture that demands a single specific god is for everything, everywhere, for everyone. They will be taught, perhaps as a highest commandment, that no other gods exist and not to tolerate those who would disagree.
Once this meme set takes hold in a culture, crusades are inevitable. If that culture gets benefit from expansion and conquest as well, it will just create a positive feedback loop.
Note that the meme set and psycology of intolerance needs to be combined with success and power and some initial impitus of expansionism. If these people are powerless and instead are the ones eing conquered, then sticking to their idea of a single god will instead prevent them from assimilating to the other culture. They will retain a strong cultural identity which will keep these ideas alive, but will keep the group separated and oppressed rather than blending in after a few generations.
So, you just need the culture in question to be able to conquer others, and have some other reason to get started. Regardless of what they have previously said about killing and virtue etc. the reality will be bent to enforce the political situation and the people will naturally gravitate to true intolerance even if scripture doesn't actually say to kill all infidels. The reality we see in the actual world is that scripture of successful main religions is complex and something can be found to justify any position, rather than the other way around. If the bulk of it is oral tradition and later interpretations and commentary, it is even more amenable to that.
I think what you are looking for is the ways in which the real docterine is extended from or even contradictory to the most central standards document. I suggest looking at real history for the many ways in which this happens.
Off the top of my head,
choosing which texts to canonize. The one that says worship is a private thing and people should do it alone and many do it anywhere will get left out by an organizing priesthood caste wanting central public stuff and a priesthood caste!
cherry picking the readings. A huge amount of conflicting material will be boiled down and presented by the priests and government to support whatever view they want. Even in a day when people are literate and could read the whole thing, people seemingly do the same thing on their own!
tiered scripture: besides a small most-sacred text, you can have part that is written, part that is oral, and a body of secodary work that “interprets” the original. This makes it even easier to direct as needed and shift with the times.
teach the secondary material as primary. You say “this is what the diety wants/this is what we must do” and trace it back to interpretations in the main scripture only as advanced study.
OK, with full monotheiem the very existance of other gods can be seen as herisy, so that makes things easy. When the expansionist culture acknowledges the existance of other gods, we have to look at what aspects make it so.
The panthon can be arranged in a strict hierarchy, mirroring the political system of the culture that goes conquering. The one particular god is the boss, his area of speciality being to be the cosmic emporer. Other gods have specificy duties and areas, but now there is also an area of command!
The particular traits can be expanded in geography, so that god X isn't just the god of this valley but is a harvest god in general and applies everywhere.
Just as different regions have their local leaders who now need to be subservent to the new empiror, the other people’s gods mirror that structure and are local subservent gods.
Over time, the culture can shift gradually toward a monotheistic mindset by classifying the boss god as a different thing, so the others are no longer gods but go by a different name such as archangles. Different original gods can be rolled up into different faces of one. Gods that are not part of the new system can be called demons and the culture refuses to admit them as gods even though they have the same properties—just a different label.
The gods may parallel the political structure and sgrugles of the larger region. One true king, even though that other guy seems to be governing over the mountains… so it is with their respective gods.