A thought from the holy Reb Tzadok of Lublin, in his work Tzidkat HaTzadik[1]:
The essence of Judaism is being referred to as a “Jew.” This is expressed in the verse (Yeshayahu, 44:5), “This one shall say, ‘I am the Lord’s,’ and this one shall call himself by the name of Jacob, and this one shall write [with] his hand, “To the Lord,’ and adopt the name Israel.” The only advantage of the individual is that he is called “Israel”—and this is enough.
This idea is expressed in another Talmudic statement concerning the sins of a convert. The Talmud (Shabbos 68b) states: “A proselyte who is converted in the midst of Gentiles and performs many labors on many Sabbaths, he is liable to one sin-offering only. And he is liable to one [sin-offering] on account of blood, one on account of heleb, and one on account of idolatry.”
Clearly this convert is unaware of the most principle laws of the Torah—Shabbat and idolatry. That being the case, with what is he considered a convert? However, by taking on the identity of Israel he is already a convert, although totally ignorant of the entirety of Torah.
It is for this reason that one must sanctify one’s life and not convert to Islam.[2] This is notwithstanding that Islam is not idolatry, they are strict of the laws of adultery and forbid murder—the three laws that one must die for.
However, one must sanctify one’s life in order not to lose the name “Israel” and “Jew.” For, this is equal to all of the Torah and the three cardinal sins.
This is the merit of the earlier generations. Although they were sinful with all sins including idolatry, they never abandoned their identity as Jews.
[1] #54. Missing due to censure in many prints.
[2] Shut Radvaz, Sec. 1163. Vol. 4. Section 92. See however, Iggeret HaShemad from Maimonides.