The historical separation between the two beliefs doesn't mean that they aren't practicing Judaism.
Actually, to answer you in a diffeent way. The path that the original Jewish Christians created for themselves was/is not Torath Mosheh. This is by their own admissions, by the admissions of the Church Fathers, and even modern day movements that claim to base themselves off of them. Thus, there aren't any Jesus followers who have ever historically declared themselves to be doing so Torath Mosheh and no one in the New Testament ever claimed to be Judaism.
The practice of all those in the modern day messianic movement, sacred name movement, nazaerite movement, hebrew roots, etc. by their own definition are not based on the Torah/Halakha given at Mount Sinai by Hashem and thus they are not valid as Torath Mosheh or Torah Judaism based. This explains why these movements started in the 1960's with their previous model calling themselves "Hebrew Christians" which started in about the late 1800's and it explains why the Jewish Christian Jesus beleiving element died out two centuries after it started leaving no direct Jewish heirs. I.e. no Jews today claim descent from Jesus or any of his disciples or even any of the people who are actually named in the New Testament.
The Torath Mosheh and Torah based Judaism response is united in one simple truth about this topic. Those who beleive in Jesus, in what ever format, have the freedom to do what ever they want to do - in thier own spaces. Their predecessors of the Jewish Christian/Jesus following persuasion seperated themselves out of the Torath Mosheh communities more than 1,800 years ago for a reason and that is the way they preffered it. By like token, the mitzvoth that Hashem gave to Torath Mosheh Israelis/Jews was to stay away from beleif systems that are found in Jesus based texts and sects/groups.
Things tend to work out way better when we Jews are able to avoid being to closely entrenched in Christian issues (texts, philosophy, etc.). Christians don't need us to accept, respect, acknowledge, or agree with their religious beliefs. We surely don't need Christians to to accept, respect, acknowledge, or agree anything we Torath Mosheh and Torah based Jews do. Thus, we are no threat to the Christian/Jesus centered belief and a healthy distance is the best way to keep it that way.