Secondly it is one of the least objectionable hymns from an Islamic theological perspective. (No talk of Trinity, Incarnation, Crucifixion, etc.)
In fact, I would suggest that it makes a very good "ashurah hymn" (see day after day after day...) If you go by the most rigorous Sunni textual standards, Ashurah celebrates God rescuing the Jews from the forces of Pharaoh. And of course for Shias it commemorates the death of Hussein. But there are also soures which associate the day with other acts of God's mercy throughout sacred history, including the landing of Noah's ark, the healing of Job, the ascencion of Jesus and other events which are all superimposed on one another much as they are in the song:
God gave Noah the rainbow sign
"No more water but fire next time"
Pharaoh's army got drownded
O Mary don't you weep
The same God who is willing to enter powerfully in history and drown an army to save a nation, is the same God willing to raise one person to comfort a crying woman.
You Tube: O Mary don't you weep (1930's Georgia fieldhands)
You Tube: O Mary don't you weep (Bruce Springsteen)
You Tube: O Mary don't you weep (Yolanda Adams tribute to Aretha Franklin)
Lyrics to O Mary don't you Weep (Springsteen version)