Those who follow a strict vegetarian diet are in fact allowed to eat butter as it is not a type of meat in any sense. People who are vegans however are not allowed to eat butter because of the fact that it is an animal byproduct.
Many people confuse vegans and vegetarians because they seem similar, though there are some very distinct differences which are important to take note of. Butter is not considered to be a meat like chicken or beef so it is therefore allowed for vegetarians. Vegans are not allowed to anything that comes from animals and since milk is used to make butter, it is not allowed.