In the poem "Street," is there a deeper religious meaning that relates to Mary Magdalene?

I think that reading the butcher's daughter as a reference to Mary Magdalene is a bit of a stretch. Certainly the woman in the story is an unusual character. One notes the white of her clothing, a color that normally symbolizes purity, contrasted with her knife and the blood dripping from it.
In fact, this recalls the image of ancient (pagan) Celtic priestesses who wore white and would dispatch sacrificial victims with knives. Given that Eiléan Ní Chuilleanáin is Irish and knowledgeable about Irish history and literature, the notion of this as a reference to a pre-Christian Celtic tradition seems more likely than reading the butcher's daughter within a Christian context. 
Reading the poem as referencing a Celtic tradition would position the butcher's daughter as evoking an image of Ireland before English conquest and the man admiring her as an Irish patriot. The blood would evoke Ireland's history of suffering and conquest.