Did they put their differences aside? Was there any lingering animosity between soldiers after/during? Or was that exclusive to northern and southern politicians?
Obviously, it varied significantly from a common soldier to a leading General. Many southerners considered northern military rule oppressive and did not support equal voting rights. However, several significant leaders overcame their differences with their former enemies.
Joseph Johnston who surrendered to Sherman apparently did not permit people badmouthing Sherman. He famously died after developing pneumonia because he refused to wear a hat during Sherman's rainy funeral.