My baby is 4 months old and strictly breastfed. why was there a long, green, mucusy, stringy thing in her poop?

Stool varies: Stool color, consistency etc. Varies with diet, hydration, viruses, etc. Granted the baby's diet hasn't changed, but sometimes the poop is effected by what mom eats. Sometimes it's a virus that turns stool green. The most important thing is that the baby continues to nurse/drink/void/stool well, and is acting normal. If everything else is fine, don't worry about a little green poop.