Thousands of men from the South left their native states and joined the Union army. How were these southern-born men treated when they enlisted in the Union army? Were they regarded as heroes for preserving the Union, or were they regarded with suspicion and contempt (like the Japanese-American troops of WW2)?
It's hard to say how individual soldiers in individual outfits were treated, but a look at general officers might be instructive.
Gen. George Thomas of Virginia, for instance, is considered one of the war's great generals ("The Rock of Chicamauga), although his reputation suffered from a common belief that he was methodical to a fault, and the fact that he served in the less-publicized Western theater. His men held him in great esteem, partly because he was deliberate and careful on both offense and defense, and did not waste lives in needless actions.
He made a fast friend of William Sherman, who while also remarking on Thomas's "slowness," acclaimed his skill and his dedication. Both Sherman and Grant lauded Thomas for his loyalty to the Union, which cost Thomas most of his familial relations and friendships. He was shunned in his home state even after the war, and was buried in New York after his death on duty in California.