My friend and I got into this as she prefers the Southern version (cause Elvis), while I prefer the one that talks about beating up traitors, and because I think the Northern lyrics are cleverer.
My points: While the song never outright mentions slaves, they are conspicuous in their absence. The first line literally names the South "the land of cotton" as if that were something to be proud of, nevermind who is forced to pick it. To me it is as bad as naming Xinjiang the land of cotton today (just lost 5 social credit points there).
Furthermore the whole "in Dixieland I'll take my stand/to live and die in Dixie" is certainly meant to appeal to an audience becoming increasingly steeped in Southern nationalism, and its place as a national anthem of the Conferacy makes it somewhat uncomfortable, especially when Elvis puts it next to Battle Hymn of the Republic.
Lastly as it was originally sung by minstrels in blackface (not my objection, that was common at the time) "I wish I was in Dixie" could give the impression that black prople long to go to the South, in the spirit of arguments that blacks were better off in the South than the North, which seems downright insulting.
Her points: It is originally a Northern song, that the South adopted it doesn't change its origins, and the composer wasn't pro-seccessionist, it simply spread from the North to a receptive audience.
The land of cotton is just a description, lots of regions have somewhat historically problematic names. Meanwhile the North could be called the land of tobacco or corn or whatever.
The song doesn't glorify the South, it satirises the idea of willing slaves with the minstrel lyrics being intentionally comedic. Most Southern versions did away with the black speaker.
Taking ones stand is a common symbol in American music from the War of Independence and the colonial mindset of self-reliance, it isn't a literal call for secession.
Please bear in mind that this debate is purely academic, neither of us are American of any stripe and I don't particularly care if anyone sings Dixieland at all. This was simply two different perspectives on which version of a song is better in a friendly argument in which I fully respect her points as potentially valid (though not vice versa!)
TL;DR I believe the song has a negative history, and understandably wouldn't be well recieved by many today, while she thinks it has been redeemed by its origins and subsequent pop-culture usage.
In simplest terms you are correct, and she is wrong. The song already has gone through sanitization, originally being written in a pantomime of a 'slave dialect', while comedic, this was not exactly satire. And more importantly it fits firmly within a broader tradition of minstrel shows and music, that is very, very racist, and of course insofar as it survived past the war it was by explicit association with the South and the Lost Cause... For more on this, including some discussion of Dixie specifically, although as just one example of many, check out this older answer.