Anything short of a clear landslide for one of the two candidates is going to result in a seriously tense/chaotic situation. Best to hunker down and hope the civilians sort their shit out before giving an order you know is going to result in a lot of resentment and formerly good, dependable people being locked up for insubordination (best case), or entire organizations dissolving in an orgy of mutiny, violence, and/or desertion (worst case).
As far as a split goes, it wouldn't be "clean." Unlike in the 19th century, individual units aren't constituted from people drawn from the same geographic area. There's a centralized bureaucracy managing personnel, so most units really are a cultural melting pot made up of people from all over the country. So I don't see the military splitting, I see it falling apart.
I just hope that the outcome will be chrystal clear, hopefully democrat. And that if it is not unit cohesion is strong enough to prevent the US forces from falling apart.
Which could, if you ask me, be a risk in case trump wins but it is rather clear that the election was fradulent (not saying it will be, but let's assume for the arguments sake it was). In which case the military would have to decide which "president" to follow, or to follow congress, or the senate, or someone else. Which could tear the military appart, let alone to speak of the national guard.