Let's turn it around- do you think it is arrogant for me to say that Christians who do not accept Jesus as their savior are no longer Christian?
I know of many observant Jews who also believe that Jesus is the Messiah. They are no less Jewish because of that belief.
By definition, anyone who accepts Jesus as the Messiah is not an observent Jew.
Where did this "definition" come from? It obviously is NOT from the more ancient teachngs. Just because some Jews believe Jesus is the Messiah, why do YOU think you can declare them "not Jewish"? Isn't that for GOD to decide??
A Chrisitian is anybody who beleives and accepts Jesus as the Messiah, if you don't believe in Jesus your not a christian bottom line.