They’re just a throwback to 1st century Christianity. The early Christians considered themselves Jewish, too. They were kicked of the synagogues and told they were no longer welcome there. Hasn’t changed in 2000 years. A Jew that accepts Jesus is no longer practicing Judaism, no matter how much they argue otherwise.
Nobody today is practicing Judaism as it existed at the time of Christ. Back then, temple sacrifice and burnt offerings, performed by a Levitical priesthood, was Judaism.
Christianity (i.e., the Judaism of Jesus) originated with the resurrection.
The Jews of today practice Rabbinical Judaism (aka, Talmudic Judaism), which originated after the destruction of the temple, nearly 40 years after Christ's resurrection.
Christianity is older than Rabbinical Judaism, though they share common roots.
It's misguided for Christians (including Messianic Jews) to mimic Rabbinical Jews in an attempt to "be more like Jesus." Christ founded the Christian church. We've no need to look anywhere else for guidance on how to live.
But yet, a Jew who is an atheist can be accepted as fully Jewish.