I want to rephrase this to be less leading (acknowledging it wasn’t necessarily the songwriter’s intention), and I hope it doesn’t trip up anyone writing a nice detailed response:
“Why did she regularly perform ‘The Night They Drove Old Dixie Down,’ which could be seen as sympathetic to the confederacy?”
So, before I get into this I just want to clarify that Joan Baez is still alive, so the title should probably be in the present tense.
Okay, so the first thing to note is that the song was written in 1969 by Robbie Robertson of The Band. He was Canadian, and although he researched the Civil War when writing the song, he was probably less knowledgable than your average American of the time, saying 'they dont teach that stuff in Canadian Schools'.
The song was inspired by Robertson meeting the father of The Bands southern drummer, Levon Helms (who also sung the song). Helm Sr said 'the south will rise again', which made Robertson want to 'write lyrics about the Civil War from a southern family's point of view'.
The reason I bring this up is to say that the song was not originally written as some kind of Confederate anthem, or rallying cry for southerners. It was a story song about an ordinary man in a war, written by a Canadian. For what it's worth, The Band was Bob Dylan's backing band (hence the name) for years before writing the song. Dylan of course started his career as a political, anti-war, anti-racism folk singer with tight bonds with Joan Baez.
Moving on to why Joan Baez sung this song, and what it meant in the context of a protest singer. I'd like to quote Brooke Gladstone, a journalist and author, as she sums up a common take on this quite succinctly:
"I'm guessing that she didn't see the song as mourning the Confederacy, but as an expression of class consciousness, and... ...perhaps a protest against the conscription of poor and marginalized young men into fighting a war, the Vietnam War, that affluent people could get out of"
Baez starting singing the song in 1971, while protest movements against the Vietnam War were in full swing. Music critic Jack Hamilton writes that the song is 'an anti-war song first and foremost, and one that is definitively rooted in the Vietnam era'.
Hamilton also quotes historian C. Vann Woodward, who noted (at the outset of the Vietnam War) that the American South was 'the only part of the United States to have experienced military defeat'. The implication being that the Confederacy in The Night they Drove Old Dixie Down represents America as a whole in Vietnam.
Again, just as Robertson and Baez weren't purposefully honouring the ideology of the Confederacy, this comparison isn't meant to honour the ideology of the USA in Vietnam, but to call attention to the plight of the working class, often conscripted soldier, and the unnessecary destruction of the war itself.
Conversely, a different reading of the song could see a comparison to the Confederacy and the Vietnamese; seeing their homes and lives threatened by an invading force.
Essentially what it comes down to is that the song is not about the ideology of either side in the Civil War, but 'the experience of war for those who are asked to give themselves up as collateral damage for the powerful, a central concern of the Vietnam-era anti-war movement.'.
Of course, the song is often taken by some ti be a pro-Confederate Anthem, and it's easy to see why. Early James performed the song at a tribute to The Band in 2020, and felt he had to change some of the lyrics to make it 'a little more palatable'.
But the short answer is that the song was written by a Canadian about the experiences of a poor southern family, and sung by Joan Baez as a comment on the Vietnam War - specifically about the experiences of working class soldiers.
Sources:
https://americansongwriter.com/band-night-drove-old-dixie/
And the song:
Firstly, the historiography of the American Civil War - the way that people understand the historical narrative and the motivations for why things happened - has changed since 1971, when Baez covered the song. For a century, the 'Lost Cause' myth was prominent in the way that historians - and educated people reading those historians, as Baez would have been - discussed the Civil War. The Lost Cause myth systematically downplayed the racism of the South and the role of slavery in the war. Part of the story of the re-evaluation of something like 'The Night They Drove Old Dixie Down' as a 'confederate sympathizer song', to use OP's words, comes down to the filtration of these changes to the understanding of the American Civil War in the ordinary person. These days, unlike in 1971, the Confederate flag increasingly gets seen as a hate symbol, and statues of Confederate generals get torn down, etc. For more on the Lost Cause myth, see /u/Georgy_K_Zhukov's review of the Ken Burns Civil War documentary, which is very problematic in its adoption of Lost Cause mythology, or /u/The_Alaskan's comment on why history was written by the losers in this particular case.
In regards to Baez's intentions in covering the song, in her 1987 memoir And A Voice To Sing With, the most she says about her 1971 recording of 'The Night They Drove Old Dixie Down' is:
As I was leaving Vanguard, we released “The Night They Drove Old Dixie Down,” which became my only big “hit” to date, going up to number five on the pop charts and staying in the top forty for fifteen weeks.
While memoirs are not necessarily reliable documents, it's notable that she neither tries very hard to defend the song, nor trumpets what is her biggest hit. This is curious to me, but my judgement is that it likely comes more from Baez not wanting to indicate that such success matters much to her, than anything about the politics of the song.
However, this does answer the question of why she regularly performed/performs the song: it was her biggest hit. For a certain chunk of her audience, Baez not playing the song is like going to see Fountains of Wayne and them deciding not to play 'Stacy's Mom'.
Books about Baez that I can find also give the song relatively short shrift. A 2020 biography of Baez, Joan Baez: The Last Leaf by Elizabeth Thompson, also doesn't comment on the politics of this particular song, for whatever reason. Neither does Markus Jaeger's dissertation Popular Is Not Enough: The Political Voice Of Joan Baez, as far as I can tell. It is surprising to me that Jaeger doesn’t comment on the song, in particular. But then Baez having a hit in 1971 is sort of incidental to her career in a way - she built a following being connected to a folk movement and gets her credibility/authenticity from that, not from the hit.
There is a mention of the politics of the song in a 1974 journal article by Cheryl Irwin Thomas about Baez's methods of political persuasion:
Baez's "The Night They Drove Old Dixie Down" functions in the same manner. The speaker of "The Night They Drove Old Dixie Down" is Virgil, a Civil War rebel, whose brother was killed by Yankee soldiers. Through the song today's "rebels" are given a sentimental trip into the past, which allows them to associate their cause with the martyred South and draw upon emotional associations. Virgil's mournful lament, "They should never have taken the very best. . ." refers to his brother as well as to the South, and this lament appeals to contemporary movement followers who can interpret "the very best" as the many young men killed in Viet Nam or even the many imprisoned draft resisters. Although interpretations are not specifically stated, the historically oriented song can create emotional associations in a contemporary setting.
The album her cover of 'The Night They Drove Old Dixie Down' is from was a double album called Blessed Are..., and featured cover art which depicted an open casket military funeral. The cover art was created by Baez's (very recently ex-)husband David Harris, a prominent anti-Vietnam war protestor who was imprisoned for objecting to his conscription (and who was released from prison in 1971, the year of Baez's cover). Given the choice of cover art, and the topic matter of 'The Night They Drove Old Dixie Down' (the big hit off the album, of course), it might be that Baez perceived the song to be an anti-war song of sorts - certainly Cheryl Irwin Thomas in 1974 takes that as the message of the song. But of course, what is intended for a song by the author or the performer, and how it is taken by the public: these can often be radically different, as Bruce Springsteen discovered when Ronald Reagan embraced 'Born In The USA'.
The cultural historian Jack Hamilton, who wrote insightfully about the racial politics of 1960s rock and soul in the book Just Around Midnight, wrote an opinion piece for Slate magazine in 2020 about the meaning of 'The Night They Drove Dixie Down'. Hamilton is dismissive of the song as a piece of history:
I could point out that as a piece of writing, it’s always struck me as wildly overrated. Its grasp of history is Wikipedia-deep and full of the sort of cloying specificity that’s a hallmark of third-rate historical fiction.
Hamilton takes pains to point out that, as a character song, you are not necessarily meant to take the narrator as the hero of the song. He also points out that the song is not necessarily pro-South and is in fact quite tonally ambiguous:
It’s about the devastation of war as experienced from the losing side, but, with the possible exception of the line “They should never have taken the very best” (an ambiguous they that could refer to either the Confederate war machine or the Union army), which prompts some audible applause in The Last Waltz, there’s not much in the song that rings as an explicit endorsement of the Confederacy. In fact, the song’s chorus refers to “bells ringing” and “people singing” and is notably major-key, almost triumphant.
That tonal ambiguity comes across differently in a world that has increasingly dispensed with the Lost Cause myth, where historians increasingly firmly sees the core of the Confederacy as being very strongly about preserving slavery, and that even poor clueless grunts in the Confederate army like Virgil Caine were knowingly complicit in a terrible moral failure. But in the 1960s/1970s, this historiographical process had not happened, and someone like Joan Baez - who performed on stage at the same event where Martin Luther King gave his 'I Have A Dream' speech, as a prominent supporter of civil rights - obviously had no qualms about performing the song, where a similarly political singer in 2021 very well might.
Hamilton goes on to argue in the Slate piece that, while Robertson's motivations for writing the song are unclear, it would have resonated at the time as something of a class-conscious anti-war song, along the lines of 'Fortunate Son' by Creedence Clearwater Revival, which was using the topic of being on the losing side of a battle to make comment about the then-very-live Vietnam War. This was certainly Irwin Thomas's interpretation of the song in 1974.
In conclusion, I suspect that as far as Baez is concerned, seemingly, it was a largely good folky pop song with some commercial potential, the same way as, say, The Beatles' 'Let It Be' might be (which she also covered on the Blessed Are... album). As a singer, Joan Baez was intensely political, and I don't doubt that she very often considered her song choices carefully for their ability to impart a message. But if this was the case with 'The Night They Drove Old Dixie Down' - if she was singing it as another anti-Vietnam war song - it's not something she has discussed, as far as I can tell.
But while it's possible she was making a statement here....well, just as Freud said that sometimes a cigar is just a cigar, sometimes a song is just a song.