From the oath keepers website

Oath Keepers is a non partisan association of currently serving military, peace officers, fire-fighters, and veterans who will fulfill our oath to support and defend the Constitution against all enemies, foreign and domestic, so help us God.

Our oath is to the Constitution, not to the politicians, and not to any political party. In the long-standing tradition of the U.S. military, we are apolitical. We don’t care if unlawful orders come from a Democrat or a Republican, or if the violation is bi-partisan. We will not obey unconstitutional (and thus unlawful) and immoral orders, such as orders to disarm the American people or to place them under martial law. We won’t “just follow orders.” Our motto: “Not on Our Watch!” or to put it even more succinctly, in the words of 101st Airborne Commander General Anthony McAuliffe at the Battle of the Bulge, “NUTS!”

There is at this time a debate within the ranks of the military regarding their oath. Some mistakenly believe they must follow any order the President issues. But many others do understand that their loyalty is to the Constitution and to the people, and understand what that means.