The milky strands and translucent shapes you find in raw unpasteurized vinegars are called “The Mother” of vinegar. It is perfectly safe and is in fact a sign of a genuine, unpasteurized, naturally-processed vinegar.
“The Mother” (so-called because it actually creates the vinegar) is made up of the harmless vinegar bacteria called “Acetobactor.” This is what turns the juice, cider or wine into vinegar. “The Mother” has enjoyed a widespread folkloric past and unfiltered vinegars are thought to be particularly beneficial to the digestive system.
Refrigerating vinegar will slow or stop the formation of “The Mother.”