This is a question I used to discuss with a history professor of mine who was a Civil War expert. He got his Phd from Berkeley in the 1970s and Eric Foner was on his dissertation committee so you can guess what his politics were (very Meatheadish). He always insisted there was no evidence that blacks actually fought on the Confederate side in the Civil War. His arguments were the same as the ones Levine uses in the Post article. I’d ask him about some of the evidence to contrary (like the stuff cited by Williams and some of the responders to Levine) and he would dismiss it as unreliable or fabricated. He could never effectively answer my questions like why black historians in early 20th century America would want to forge evidence of blacks having fought for the Confederacy.
My tentative conclusion on this question has long been that the Confederate Army had a kind of policy on this question equivalent to “don’t ask, don’t tell.” The official position of the Confederate political and military leadership does seem to have been to bar blacks from service. However, it’s also pretty well established that the policy was at least at times disregarded. There would seem to be two ways in which this might have occurred. One, local military commanders could have simply disregarded the policy when raising local forces out of military necessity. The other possibility is that the upper levels of Confederate leadership maintained an official policy of racial exclusion regarding military service as a means of avoiding public controversy, upholding the white supremacist ideological outlook that virtually all whites had in those days, and possibly avoiding unrest by white soldiers, but winked at military organizers and commanders who disregarded the policy in their actual practice (and possibly even encouraging them to do so).