In the original sense, a "conservative" was someone who avoided change and only made it after careful consideration. Chesterton's fence is a commonly given example: https://en.wikipedia.org/wiki/Wikipedia:Chesterton%27s_fence

The word "conservative" is currently being applied to the Republican party, who are reforming the US as hard and fast as they can manage, without careful consideration. A "move fast and break things" approach is about as un-conservative as one can be.