The Rebbe's teaching on Jewish identity, mesirus nefesh (self-sacrifice) and Kiddush Hashem:
What makes a Jew. Being Jewish is an unchangeable essence, not a matter of belief or declaration (IK 10859), and faith and core values are innate in every Jew — education can only cover them temporarily (IK 8333). Jewish identity depends solely on descent from a Jewish mother or on halachic conversion; declarations and civil registration cannot change it (IK 6714, 8344). Jewish identity cannot be separated from Torah and religious life (IK 7542), and it endures through practical observance of mitzvos, lived out every day (IK 5362, 9854). On the "Who is a Jew" question in Israeli law, see Land of Israel – Who is a Jew, conversion and public Shabbos.
Standing firm. Even when Jews seem few or weak, or face ridicule for their faithfulness to Torah, they must stand firm (IK 1062). Maintaining one's Jewish identity requires inner strength rather than conforming to others (IK 6798), and authentic Jewish pride earns the respect of others (IK 9954). Israel's true strength lies in its eternal spiritual values, not only military might (IK 1033). Torah study and daily mitzvos are the true pillars of Jewish endurance through history (IK 6001, 5771), and Jewish survival depends on Torah education from childhood (IK 9393, 9462). Avoid interfaith events that compromise commitment to Jewish faith (IK 1415).
Mesirus nefesh. True chinuch combines understanding with readiness for self-sacrifice (IK 1288, 1289). Becoming bar mitzvah means accepting G-d's sovereignty, not only intellectual maturity (IK 1521). True mesirus nefesh includes one's daily struggles, not only extraordinary moments (IK 5830), and dedication to Torah should persist whatever the external circumstances (IK 2363). A mitzvah done with self-sacrifice and joy is elevated far beyond its material value (IK 8625).
Kiddush Hashem. Upholding Torah standards in public — a proper mechitzah, Cholov Yisrael, public Shabbos — is a sanctification of G-d's name (IK 3453, 3888, 6097). Living without danger brings a greater responsibility to spread Judaism actively (IK 9383, 5601).
See also: Land of Israel – Who is a Jew, conversion and public Shabbos; Marriage – Intermarriage; Jewish outreach – Reform, Conservative and interfaith questions.