I know I use the term, but I don't believe it's a commonly understood one. Maybe we could unpack what we, in this community, mean by the word.
And, just to get the ball rolling, here's my thoughts on the subject:
I view syncretic as being a particular approach to the worship of the gods. It has elements, at times, of universalism. It allows cultural borrowing and overlap, much like the Romans did with egyptian and greek elements. There seems to be an underlying "all gods are one god, all goddesses are one goddess" component to most syncretic practices with which I've been familiar.
This, to me, is a contrast with eclectic, which is an intentional use of disharmonious or unlike elements to create a new whole, like making a collage. Repurposing elements so that they form a new texture, an interesting symbolic statement, and so forth.