No, I have no particular objection to Jesus as a purported historical character.
Though, his common modern portrait as a handsome clean-shaven 35 yo Nordic bourgeois with long chestnut locks and fresh white nylon frock is a pretty wild misrepresentation of a "Mediterranean Jewish peasant", as Crossan put it.
I have noticed that every group of people, of all ethnicities, portray Him as looking like them. I have seen Him portrayed as African, native American, Asian, Indian....you name it.
So why is it only the 'white' group that gets criticized for doing so?
That said, I'm pretty sure that He was probably short, had curly black hair, (which he probably wore short, as did most men of his time) was darker skinned and had pretty classic aramaic features. He probably wasn't all that handsome, either. I mean, even the bible states that he wasn't pretty.
But I don't mind if my African American neighbors have Him as black and dressed in African dress, or that my Vietnamese friends have Him with the classic Asian eyes and long, straight, black hair.
I don't see the need to get all picky about it, personally.