I would argue that the Republicans for the most part are NOT conservatives but rather mostly ideologues of different stripes
Big business types (BB) are in no respect conservative. They simply want to be free of government regulations so they can pursue profits unimpeded. They are liberals in the original (19th cent.) meaning of the word, meaning anything goes. Their ideology is Capitalism: One Market Under God.
The neo-cons (NC) are merely Cold War nationalist liberals who need a Big Enemy to justify American hegemony. Their ideology is American Supremacy.
The libertarians (L) are similar to the big business types in that they are anti-government for economic reasons, but they also promote fierce social individuality. There is nothing inherently conservative in any of this. Their ideology is personal Liberty.
The Christian Right (CR) would like to impose a theocracy. This is radical, not conservative (though, of course, they think this is how the U.S.A. got started). Their ideology is triumphalist Christianity.
The country music/NASCAR populist component (P) is nostalgic and parochial. This could be accounted as conservative. Their ideology is The American Way.
Main Street business interests (MS) are mostly genuine conservatives. They have a modest economic stake they want to protect and generally have a commitment to their communities. Their ideology is also The American Way.
The American Way is an all-purpose ideology. You could say it’s what we all learned in school. The Republicans assert it more aggressively as a partisan weapon, and a big burden on the Democrats is that they can’t refute it or ignore it without appearing to be (and being) intellectuals and elitists.
So what does it REALLY mean to be politically conservative?
First, to respect and wish to conserve valued elements of the past, considering such forms of human endeavor as learning, art, and sport as worthwhile in their own right, and these things and world we live in as a heritage worth preserving. BB, NC, L, and CR instead want to change everything.
Second, to resist economic reductionism, the idea that at the end of the day (to use a favorite business cliché), we are all primarily producers and consumers and only the bottom line counts. This is the essence of BB, and it’s amazing how they get most everybody else to buy into it.
Third, to be careful about changing institutions. The Bush administration carelessness/contempt for this is what makes it profoundly anti-conservative. BB doesn’t care, because it is effectively supra-national; NC sees consolidation of power as furthering its ends; L despises institutions; P doesn’t realize what’s going on; and MS basically doesn’t lift its eyes up.