Seeing a dog in a bright blue vest can make it look like there’s a universal code everyone else somehow knows, but vest color by itself does not have one official meaning everywhere. Different veterinary clinics, trainers, rescue groups, and owners use colored vests for different purposes, so blue should never automatically be interpreted as one specific warning.
At a veterinary clinic, a vest may be used to identify a dog that needs extra space, is nervous around other animals, is undergoing training, or should not be approached or distracted. Some service dogs and service-dog trainees also wear blue vests, although service animals are not legally required to wear any particular color. If the vest says “Do Not Pet,” “In Training,” “Nervous,” or something similar, that wording is far more important than the color itself.