Q: What do The Simpsons say about Mary?
A: The long-running animated comedy series from FOX frequently addresses various religious topics. In this area, the perspective of their writers is generally positive though critical of various distortions and abuses. A good deal has been written on this topic (e.g. Religion in The Simpsons [2000 ] by Dr. John Heeren and The Gospel According to The Simpsons  by Mark F. Pinsky).
However, there have been relatively few references related to the Virgin Mary during the show's thirteen seasons. I am aware of the following examples:
None of these incidents played a significant role in any of the episodes. In my opinion, each use envisions Mary solely as an artifact of popular culture, especially in regard to certain ethnic groups (e.g. Irish and Hispanic). This tendency is not uncommon in other mass-media productions.
Other valuable insights were shared with me by Lance Wilder, an animator with Film Roman whose projects include The Simpsons. He opined that the nativity scene in "Miracle on Evergreen Terrace" was an American cultural artifact in the same sense that brief Marian invocations are for certain other cultures. He also noted that destroying the nativity scene in this episode emphasized Bart's dangerous irresponsibility better than destroying a neutral object like a lamp. He believed the same principle was operative in showing a religious painting among the stolen art in the aforementioned episode #3F19. I've found that this technique of using Marian symbols as a comparative standard against which to measure the virtue or vice of a character has been common in the motion picture industry for some time.
Finally, Mr. Wilder could neither confirm nor deny any special significance to Lisa's apparel in the aforementioned episode #8F01. The mascot for Columbia Films dresses similarly and might also be the source of the reference. If it is indeed a Marian allusion, it is noteworthy since Lisa delivers an important message to the public in this episode and could then be explicitly identified as a symbolic Marian figure.