Most accurate answer is probably "it depends upon who you ask."

As others have pointed out, there are many amateur folklorists, and many academically trained folklorists, and sometimes the two are even the same (ie end up going on for further formal study and training in the academic disciplines of folklore, cultural anthropology, or ethnomusicology).

There seems to be some confusion about whether folklorists actually study folk music. Many do, many don't. Folklore and anthropology don't study/collect music cultures exclusively, and many in those fields never study/collect music at all. However, ethnomusicologists always do both if they are formally trained. I have yet to meet anyone who has referred to themselves as an amateur ethnomusicologist--it seems to be a title only those who have university training/degrees in the field seem comfortable wearing.

As to the "only if it is traditional" definition, this is largely a myth. Academic and amateur folklorists now study the contemporary folklore of many cultural groups, from corporations to royalty--not just "the common people" by any means. That aspect of the "definition" of folklore is as outdated now as is the term "antiquarian" (which is what cultural anthropologists and folklorists were called before they were called folklorists and anthropologists).