The Mad Cultists are enemies in Earthbound. This is the only game that they appear in.
They are Blue Men with little blue paintbrushes. In the Japanese Version, there were two marks over there eyebrows, which looked too much like a famous Japanese Group, so Nintendo removed it in the English Version.
These are normal people who are under the control of the Evil Mani-Mani Statue. There are many of them, and only a few actually stay around. For some reason, the statue wants everything to be blue, so that is exactly what happens. Later, this group of people will find Paula and kidnap her. It is truly unknown why they did this, but it is probably because they are brainwashed, and she is one of the only people who can defeat Giygas and the statue.
Their leader is Mr. Carpainter. He doesn't look like the other ones, and he uses many different attacks. His signature attack is the Crashing Boom Bang attack, which generates lightning. This will not hit for anything if you have the Franklin Badge, which you must have to fight him. Apparently, he just wants to be a normal person. He will give you the key to rescue Paula.
Their base is in Happy-Happy Village. They are not seen afterwards.