They fought their "country". The government of their home WAS their country. They were traitors all.
Loyalty to one's home is the highest loyalty there is.
I recommend to you a movie:
"Decision at Daybreak"
A German soldier, captured by the US breaks from the line of prisoners, and tells the supervising US officer that he is a US agent. That there is a trap set for the US ahead at a river crossing. The supervising US officer wants to put him back in the POW cage where he would be murdered. Fortunately, cooler heads prevail. Though he has a set of code words that would confirm his identity at Army headquarters, because of the problems with war, chaos, and radio communications, the Brigade commander has to make up his own mind on the truthfulness of the soldier/agent.
A key aspect is why he would be helping the Allies against the Germans. He had infiltrated an SS unit, who would have cooked him over a slow fire if they had known.
No, my dear, loyalty to home is not the highest. When your home government has been taken over by murderers, perverts, thieves, and psychopaths, as the German government had been, and as the Confederate Government had been, there is no loyalty owed to them. In like manner, when State governments disregarded their obligations, and their limitations under the US constitution, they lost any legitimate claim to the loyalty of their citizens.
Even the so called "Confederate Government" did not hold that State loyalty was paramount! They assigned Pemberton, from Pennsylvania to command of Vicksburg, which they would not have done if State Loyalty was paramount.
The leaders of the Confederates had no legal case. They knew it, and didn't make one. They thought, in their cowardice, that all men were cowards, and tried to frighten the US government from making the effort to end their rebellion. All men are not cowards, and so they lost.
Another movie you may check is "Winchester 73" with Jimmy Stewart, that discusses the matter of loyalty and justice.
So my subdivision governing council is where I should concentrate my loyalties? I think that George Washington had something to say about that. But hey, what did he know?