I’ll go on record as having a neutral accent or possibly a mid-Atlantic accent. No on can identify where I grew up based on my accent.
When I want to be funny or sarcastic, I can pick up something that can be construed as a Texas twang.
Maybe the Southern accent is subtle or different enough it can coexist with singing?
It's probably more the relative weight of text (lyrics) v the melody and rhythms of speech or song, and on top of that then the regional accent.
There are assumptions your ear begins to make in terms of expectation, but in song it can be mostly that the words hang together with the beat, and your brain says ok later for whatever words are being sung. It's why we can appreciate pop or rock music that is sung in another language, but soon grow tired of someone telling us the news on TV in a language we don't get. But it's also why people like having a translation of the libretto handy during performance of an opera. When music alone doesn't tell the whole story, understanding the words certainly does matter.
In song, and more or less heavily depending on genre,
the words still matter but the beat prevails and so for example in a scripture-themed motet there are parts of words than would be pronounced in speech but are elided or not sung in performance. For instance, the Purcell song based on Psalm 130:
Plung'd in the confines of despair,
To God I cried with fervent pray'r:
O lend to me a gracious ear;
Not sunk so low but thou canst hear.
Now if the beat in that music had been different, it's possible the word "plunged" might even have been sung as "plung-ed". As long as you understand or can read English, you'd still get the meaning of that text no matter which way sung.
Compare and contrast to rock or pop -- say US southern rock-- where what's different is MOSTLY the fact that a regional accent overlays the pronunciation of words in the lyric, which pronunciations are still influenced at root by the dictates of rhythm and melodic line. Take The Allman brothers in Come On in My Kitchen.
You better come on into my kitchen
'Cause it's goin' to be raining outdoors
Now when The Allman Brothers perform this, you may hear that second line as
cuz it's gone to be rainin' ow-dohz
And of course that's if you're even paying attention to the words depending on which Allman bros tune is in play. You might just be stompin' yer boots on the floor about a minute into the thing.