This is another strain of conservativism. You start with tradition and the status quo (I mean, what the heck else are you going to start with? ! ?), and from there, you're somewhat open to intelligent, medium steps and seeing how they work out.
This was generally the philosophy of Edmund Burke in the British Parliament the late 1700s.
AHC: even with Goldwater in '64, how might Republicans (and/or conservatives) more commonly take this second approach?
As we know in OTL, U.S. conservatives have generally gone the route of advocating for sudden, abrupt change.