Except the army’s own government website explicitly says otherwise

Any member of the military has a commonly understood obligation to disobey an illegal order;

https://www.army.mil/article/47175/breaking_ranks_dissent_and_the_military_professional

Reconstruction failed because Lincoln made the mistake of choosing Andrew Johnson to ‘reach across the aisle’ and then was assassinated. And his racist piece of shit replacement did everything he could to obstruct Lincoln’s plans.