While the Torah anticipates that non-Jews will also follow a legal code of behavior consisting of the sheva mitzvot benei Noaḥ – the seven Noachide laws – the Torah neither requires nor condones non-Jews mimicking the behaviors of Jews.
According to Resh Lakish, nokhri she-shavat ḥayyav mitah – a non-Jew who keeps the laws of Shabbat is liable to receive the death penalty. Ravina clarifies this statement by explaining that this rule applies even if the non-Jew were to keep the Shabbat laws on Monday, i.e. any other day of the week.
Furthermore, Rabbi Yoḥanan teaches that nokhri she-osek ba-Torah ḥayyav mitah – that a non-Jew who involves himself in Torah study is liable to receive the death penalty, based on the passage ( 33:4) Torah tziva lanu Moshe morasha – Moses commanded the Torah to us as an inheritance. This is understood to limit the Torah to “us,” that is, to the Jewish people.
These two statements clearly demand explanation. Regarding Shabbat, the Meiri suggests that the problem is a concern lest Jews see the non-Jew keeping the laws of Shabbat and mistakenly believe him to be Jewish, which may lead them to follow his behaviors in other areas. According to the Ramah, such a person is considered “stealing” since by taking an “unauthorized” vacation he is not fulfilling his obligation to the world.
As far as Torah study is concerned, the Meiri limits the prohibition to a non-Jew who studies Torah for the purpose of arguing and disproving it. If someone chooses to study Torah in order to learn the moral values contained in it and keep its ethical rules, then such study would not be forbidden. The Rambam, in fact, differentiates between Christians who believe in the written Torah and would be allowed to learn it and Moslems who reject the sanctity of the Torah who would not be allowed to learn it. In any case, a non-Jew who keeps the sheva mitzvot benei Noaḥ will surely be allowed to study those laws that he must keep.