Jewish is a much more modern appellation than you give it credit for. My suggestion is more to do with other threads on the subject of the shroud on this site.
The genetics of Christ, if he ever existed, is open to question. Nolondil on another thread made some suggestions regarding the authenticity of the shroud concerning the shape of the face on it. I suggested deformity could account for this. Paul Mallon thought it might just be to do with the terrible beating he took before being crucified - very plausible. I just thought it would be worthwhile to put forward the notion of deformity - considering Akhenaton, and his unusual deformity and his unusual religion (for Egypt). It seemed to me that Christ could be a descendent of Akhenaton. Considering the biblical link between Egypt and Israel I see it as much more plausible than feeding the 5000 (unless it was one person called 5000) or turning water into wine (unless it was Ribena) or walking on water (without the aid of many large turtles), or literally rising from the dead - though metaphorically, it seems to me that there's another link with Egypt there.
Sorry for the humour.