It has not been discouraged. It's very common around the world today. it only started to become taboo in European societies in the mid 19th century. (pardon the anthropology word) exogamous, ie outside your immediate group, marriage has been common throughout history and people in the medieval and ancient world travelled much more commonly than people think. Even a marriage group of a few hundred people has so much genetic diversity that unless a specific genetic illnes becomes fixed in the group, like Tays-Sachs or something, it's unlikely for cousin marriage to cause problems, doubly so if there's any outsiders marrying in to the group which has almost always been the case.

This is a taboo that developed recently in European culture and isn't well founded in science. There is a small increased risk that an genetic illness already present in the partners genes will be expressed in their children. The idea that it's an ancient taboo is not historical.