Confederate VP Alexander Stephens' Cornerstone Speech pretty much puts paid to the notion that the CSA was a racial utopia, though plenty of blacks and Amerindians fought for the Confederacy. As one Union soldier put it, "If I'm fighting to free the slaves, then why are they shooting at me?"
AFAIK almost no black Confederates actually shot at any Union soldiers. The few hundred blacks who are noted on CSA muster rolls got there by one of three mechanisms-- 1. They were the slaves of CSA officers or non-coms and carried on the rolls as valets, cooks, clerks, etc the same way a free man in the same position would have been in the north. 2. They were slaves purchased by or donated to or confiscated by the army to serve as teamsters, cooks, prison guards, musicians, and such. They were on the rolls not as enlistees but as property. 3. They were free blacks, mostly used in similar ways. There were very few of these who were fighting troops, though there were some; mostly Creoles from Louisiana, and those largely artillerymen. Toward the very end of the war it was allowed for a conscripted citizen to send a slave in his stead, much as northerners could hire someone to go for them if drafted. This seems to have been very rare, however. I believe I saw somewhere that only twenty-some of these have been counted. Part of the confusion on this matter has been generated by a relatively high black population in camps for confederate POWs. This appears to have mainly come about through a couple of processes: 1. Probably half of them were captured at sea; the maritime and naval traditions of both north and south were at odds with those on land, and ships had been crewed and even officered by blacks and whites for 50 years and more. Certainly it was less common in the Confederate services than the Union, but still, probably something upwards of 5% of personnel afloat were legally black-- maybe more on the rivers. And the Union captured a pantload of crews... 2. Before emancipation it was the official policy of the Union that captured Confederate officers who were imprisoned, paroled, or exchanged were allowed to take a slave with them if the slave expressed a willingness to go. Many many of the blacks on the prisoner lists surely got there through this mechanism, rather than through capture in arms against the Union. (Sherman and Grant at various points expressed dismay at the execution of this policy, because the officers were commonly allowed to speak for their slaves, or at least to be present while the slave was asked about his willingness. Grant and Sherman wanted the slave to be queried outside the master's presence and assured that no harm would befall him if he opted not to go, and that he was under no obligation to go.) Also, very large gangs of slave labor not on the army's muster rolls were also used to build fortifications, keep canals and railroads operational and so forth, under military supervision-- including captured black Union soldiers who were presumed to be "escaped slaves" without any investigation. Most of them actually were escaped slaves, of course, but by no means all. Grant eventually prevailed upon Lee to put a stop to their use for military purposes by advising him that we was prepared to do likewise with captured confederate soldiers; white ones... In general the dubiousity of the notion that lots of blacks served the Confederacy can be seen in the several massacres of black Union units which fell into Confederate hands, and moreso in the initial policy of the CSA that any union officer found to be commanding black troops would be summarily hung. (They never actually hung any-- but only because Lincoln made it clear that any Union officer hung on such a pretext would be matched by a Confederate officer hung on no pretext at all.) It is pretty clear that the Confederates were as squeamish about a black man with a gun in 1864 as the Oakland cops were 100 plus years later...
Davis and Stephens were very squeamish about that in 1864, due to their racism. The Fort Pillow massacre in TN by Forrest's troops is a symptom of that. Lee wanted anything that would help win the war. William C. Davis excellent "Look Away!" details the short, unhappy political life of the CSA. He lets the Confederates speak for themselves. The Confederate Constitution is a 19th century version of the rise of the religious right in the late 20th century.