There are many kinds and combinations of “conservative.” From “About the term “conservative” in the link below:
Painting with a broad brush, there are fiscal conservatives, social conservatives, and limited government, constitutional conservatives. These categories do not have to overlap and even limited government and constitutional are really two tight categories. Media, however, uses the term with a heavy implication of social issues, even though fiscal and limited government conservatives exist. (In very general terms, they are the Libertarians.) Overlay these subsets with the foreign policy spectrum of isolationist to interventionist and the label of “conservative” that gets used as some obvious label is not at all obviously anything.