Nope, in most cases they are not Jews at all. Get it straight. They are offensive for trying to sell something as something else.
They are Jews, as much as anyone else. There are Messianic believers right IN Jerusalem. King David was a Messianic Jew. HE is the one who prayed and asked for the Son of God and the helper(The Holy Spirit -ruach ha-kodesh ) !
Many Jews believe in Jesus. Some Jews are in Christian congregations. Some Jews are Dutch Reformed, evangelical, Baptist!
If you are offended, that is about you, not about what is being written.