The question is how much religion actually has to do with it, as opposed to being used more as a justification for things that are a consequence of other parts of society.

Islam, I agree, has a pretty expansionistic message baked into the core scripture and tenets. For Christianity, it's more of an add-on. And anyway, humans do this kind of thing without a terribly strong religious justification; the Mongols under Genghis Kahn don't seem to have been driven strongly by religion. (Likewise with Alexander the Great.)

I'm all for giving religion the share of blame it deserves, and in some things it deserves heaping oodles of blame (e.g. dogmatic control of people's behavior in ways that are harmful, at least in modern society). But the expansionism doesn't seem to have a sufficiently strong correlation with religion for me to conclude that it plays the dominant role rather than a contributing one. (Some doubt about Islam, as I said.)