Interestingly, I have a Northern Mexican friend who told me the following version of La Llorona:

La Llorona was an Indian woman who fell in love with a Spanish soldier and became his mistress. Eventually she became pregnant and had children with him, but one day he left to marry a Spanish noblewoman. When she discovered he'd left her, she drowned her children in a river, and she's sometimes still heard and seen, wandering and crying. I always thought that version of the story was meant as a warning against interracial relationships.