Fascism and libertarianism pushed conservative boundaries.
Fascism in that it took state power beyond what conservatives would tolerate, abolishing enshrined liberties.
Libertarianism in that it would reduce state power such that conservatives couldn't use it to repress the things they themselves didn't tolerate.
Nazism and Italian fascism both always presented themselves as inherently revolutionary. Hence conservative resistance from the likes of Schacht, Heinrich Maier, Otto von Hapsburg, Churchill, de Gaulle, aristocrats of the 20 July plot and other suicide attacks.
Furthermore, at the core of fascism is nationalism which is itself strictly modernist.
Many people are so fallen in with the idea of history having an end-goal, a state of utmost perfection to which all "good" action is meant to approximate us to, that they don't see the bramble of history but a straigh narrow twig instead.