I took that oath about 38 years ago this month for the first time! Gerry Ford was the POTUS and being a good Michigan boy, I had no problems with the oath. Four years later, Jimma Carter was the POTUS and certainly influenced my decision about re-enlisting for another hitch. Reagan hadn't committed to run yet...shoulda, woulda, coulda as they say!
Today, it's an all volunteer force so soldiers, sailors, airmen, Marines and CG have a choice to either swear their allegiance to the POS at 1600 Pennsylvania Ave or not so yes, I support the Military honoring that oath!
Remember, the UCMJ doesn't require you follow an illegal order from ANY superior, even the president!