Do Torath Mosheh and Orthodox Jews know who is a Jew, according to Hebrew Tanakh?

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Recently, a challenge has been made about whether or not it is possible to identify who is really a Jew. The reality is that among Torath Mosheh and Orthodox Jews there has never been a problem in identifying who is a Jew. The reason is very simply. The definition of such was first provided by Hashem in the Torah.

Since, "Doing the will of Hashem in the way that Hashem instructed it" is the focuse of All Torath Mosheh communities thoughout history. It is by this principle that one can know when actions that someone takes is correct or based on falsehood. If your family member grew up in a Torath Mosheh household where this was the focus of how they managed their lives then he would be Jewish because he grew up with Torath Mosheh parents (mother and father), in a a Torath Mosheh extended family, and in closed off Torath Mosheh Jewish community dedicated himself to "Doing the will of Hashem in the way that Hashem instructed it."

The breakdown of how Torath Mosheh and Orthodox Jews have defined who is a Jew for the last several thousand years can be summerized by the following sources.

 

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Question: What about Jews who don't beleive in the Torah or who grew up in homes where the Torah was not kept, how are they handled?

Answer: Torath Mosheh and Orthodox follow the following that the Rambam wrote in the Mishnah Torah.

Mishnah Torah - Hilchoth Mamrim 3:3

"The children of errant [to the Torah/halakha] Jews and their grandchildren whose parents led them away and they were born among those who are in error and raised according to their conception, they are considered as a children captured and raised by them. Such a child may not be eager to follow the path of mitzvot, for it is as if he was compelled not to. Even if later, he hears that he is Jewish and saw Jews and their faith, he is still considered as one who was compelled against observance, for he was raised according to their mistaken path. This applies to those who we mentioned who follow the erroneous path of their ancestors. Therefore it is appropriate [for Torath Mosheh Jews] to motivate them to repent and draw them to the power of the Torah with words of peace."
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Mishnah Torah - Hilchoth Deoth 6:7

"It is a mitzvah for a Jew who sees that his fellow Jew has transgressed [the Torah] or is following an improper path [to attempt] to correct his behavior and to inform him that he is causing himself a loss by his evil deeds as [Leviticus 19:17] states: "You shall surely admonish your colleague."

A Jew who rebukes a fellow Jew - whether because of a [wrong committed] against him or because of a matter between his colleague and Hashem - should rebuke him privately. He should speak to him patiently and gently, informing him that he is only making these statements for his colleague's own welfare, to allow him to merit the life of the world to come.

If he accepts [the rebuke], it is good; if not, he should rebuke him a second and third time. Indeed, one is obligated to rebuke a colleague who does wrong until the latter strikes him and tells him: "I will not listen."
Whoever has the possibility of rebuking and fails to do so is considered responsible for that trangression [to the Torah], for he had the opportunity to rebuke [the trangressors]."​

It is based on that there are a number of Torath Mosheh and Orthodox Jewish organizations that were founded to help Jews return to the Torath Mosheh path. The work they do is often known as Kiruv. A few of the organizations that do this kind of work are.

Aish HaTorah
Shofar
BeEzrat Hashem.net
Hidabroot
Chabad