BLUF: Whatever each uniformed individual decides, he/she had better be on the winning side.
Now, in the event of a secession as in the original Civil War, the academic case has been made that the states, as sovereign entities that agreed to form the "United" States, they voluntarily agreed to form a union and, as a contract, had the right to break that contract should the terms not be met - i.e., "state's rights."
Since the North won - Lincoln did what he had to do to win and the Constitution be damned - suspending habeas corpus, freeing the slaves that were private property, thus denying "life, liberty, and the pursuit of happiness (read by the SCOTUS as property rights)," etc, etc, etc.
By winning, he and the federal government achieved the primacy of the federal over the individual state governments. See Smith v. Texas (or some such where the SCOTUS ruled in the late 1800s that a state can't secede). If the South had won, their argument would be the one that prevailed. Ultimately, might does make right and the victor writes the aftermath law.
In the scenario listed in the article - pretty isolated and hardly a 'mass' insurrection - it isn't a Civil War. Think New Orleans and Hurricane Katrina. Big Green roled in and sorted out a lawless situation. And the Second Amendment rights of Naw'oleans were violated wholesale at the time as just one real-time, real-world example.
A better, more realistic scenario would be a very liberal POTUS deciding to stretch (not all that much compared to Executive Actions begun under Lincoln, raped by FDR during WWII, and seduced during GWB and the current Administration) his/her powers to require registration of all privately-owned firearms under penalty of imprisonment for failure to comply.
Would sheriff's allow this?
Would state governments?
Would the SCOTUS?
What if the answer to this is "yes?" by any or all of these institutions?
Would you comply?
If, to force compliance, the National Guard was federalized in order to conduct house to house searches, all in the 'national interest,' or even the standing military was ordered to do so, then the basics for an insurrection are formed.
Would the Guard comply? Would the military?
My personal opinion is that younger troops/officers would follow these orders. I am not sure about mid-grade NCOs/FGOs. I hope (never a good basis for planning) that the senior NCOs/GOs would stop this by mass resignations and/or passive resistance.
If you are wearing a uniform currently, you have to decide what you will do. Is it a "lawful" order? You have a duty to carry out legitimate orders and an equally strong duty to disobey unlawful orders.
Better be right and on the winning side.