Matt, this is a false analogy. At the time of the WTBS, the right of secession was not settled. It had been considered by other sections of the country before the South seceded, including New England. Constitutional scholars argued about it at length.
The war changed all that. No longer is it an open question. If one or more states now chose to try it again, the vast majority would not recognize it, nor serve the cause of secession. Therefore, those remaining loyal to the United States would of course be loyal citizens, and the rebelling Hispanics and whomever supported them would be in rebellion against their legitimate government. It may be considered a fine point, but there is a difference. Stan