Judging by your tagline, this might not apply, but here goes, anyway.
Hypothetically speaking, let’s say the president has issued an executive order that all firearms in private (non military/LEO/aproved agency hands) be confiscated. Some comply, many do not. A particular group of holdouts not only does not comply, but is vocal about it.
The president orders military forces to confiscate the firearms, by force if needed, authorizes lethal force, house to house searches, etc. in order to accomplish the task.
If you were in the unit so assigned, would you comply with the order. If not, would you oppose it? How far would you be willing to go to defend the Second Amendment of the Constitution?
Next question. Suppose it was incontravertably revealed that (just for fun) the president was not Constitutionally qualified to be POTUS: that in fact, he was not a natural born citizen. As your oath is first to the Constitution, and his occupation of the office and usurpation of its powers would be an egregious violation of the Constitution, how would you react to that?
There is no cognitive dissonance on my part. None. There is conflict of interests in your scenario however.
I will answer first by stating that I do not for one second believe that scenario is remotely possible. That is NOT the same as saying I do not believe BHO is anti 2nd amendment or will not have his Justice Department take on a very anti RTKBA stance.
However...
If that was the case I would be in a conflict of interests. I would do one of two things. Either request separation based on conscientious objector status, or complete the second part of my oath and leave service at the end of EOAS.