The main point is that what is considered "judaism" today is not what it was in the mainstream sense, in the time of Christ. That is all. What began taking over, as a rejection of Christ at the time until now is what it is, mainstream. That is inarguable, since they deny Christ, and that is the heritage. A "jew" of the first century had reasons to accept Christ, and many did. A jew, currently, by definition, does not. Could a modern "jew" not accept modern judaism? Sure, it happens all the time. He isn't a "jew."
In this sense, what we have put forth (2 Right Hands and I) is accurate.
Although I quoted you, the comment wasn't directed towards you. It was directed more towards the general trend of fighting and attacking the other without trying to investigate exactly what they mean (feel free to call me a hypocrite, for I'm guilty of exactly this same thing in the past), and if that had been done, there probably wouldn't have been any disputing, for it's all over the definition of terms, but once the inclination to argue begins, the passions are involved, egos become puffed up, and neither side will admit to any wrongdoing, whether in truth, or in attitude.
So to re-iterate what was said, Jesus is a "Jew" according to bloodlines which was important in accordance to the fulfillment of prophecy. Whether modern Jews are, or are not the same people racially was irrelevant in the time of the Incarnation of Christ (Matthew 3:9), and is even less relevant now.
Jesus isn't a "Jew" in the sense that he did not identify with the Pharisees/Jewish ruling class of the day, nor would he identify with the spiritual successors of the Pharisees in modern Judaism.
If anyone has a problem with that, it's a fault within their own interpretation of scripture.