Is the use of the contracted negative form of Do, the DON'T, in reference to a singular event or action acceptable in formal writings as is in song lyrics composition?
No, he was not wrong in any grammatical way.
Note that these are song lyrics, with special rules.
These rules have to do with meter and rhyme, and in print with capitalization.
Punctuation is pretty optional, and the dialect may vary from Standard English, as songs often do.
It's funny how a greater plan Is too hard to understand Right now it don't make sense.
- [It's funny [how a greater plan is too hard [to understand]]].
- [Right now it don't make sense].
I won't go into the parse of the first sentence.
Both sentences are in colloquial American rural English,
a sociolect with some characteristic regularizations of auxiliary verbs.
Many irregular auxiliary verb constructions get regularized, like ain't as a contraction of am not.
One such is that the 3SgPres negative contraction of Do-Support do becomes don't,
instead of the irregular doesn't.
Is that what you were worried about?