I wonder, in using "Don't," if the sense of it was like when we say "Don't you love it when..." or "Don't you know it!"
It does not seem to make sense to say "Do NOT tell me that!" in this song... one can take DON'T YOU as a sort of AMEN to what is told.
It would make sense, from that view, if the two words are variant expressions of a similar thought.
On the other hand, I kind of like what is implied in "Don't TELL me, just MEET me, I now the rules already!" That sort of says, "Hey, I am a saved person, just let me in there to find Jesus and see Him face to face."