The simplest and highest thing a Jew can do is to recognize that s/he is a Jew. "I am a Jew," in Hebrew, אני יהודי. Ani Yehudi. When we look at the word Yehudi, it means, "belonging to Yehudah." When we say Ani Yehudi, we are saying that the Ani belongs to Yehudah. When we return the Ani to Yehudah, the letters of Yehudah and Ani combine forming the two names of HaShem אדנ-י and י-ה-ו-ה. The former, referred to as shem Adnut, references the Shechinah, HaShem's light filling the world, whereas the latter, shem havayah, references the fact that HaShem both maintains the creation and is infinitely beyond it.
בזה שיהודי מודה על אמיתו ומכיר בעצמו הוא מיחד יחודים עצומים - בביטוי אני יהודי משייך האני ליהודה ונעשה שילוב אדנות והוי-ה מיחד קב"ה ושכינתיה
When we acknowledge our Judaism, (that there is no me separate from my Jewish identity) turning to HaShem and saying, i'm simply a Jew, we unify the two aspects of HaShem, that He fills the world and that He is its boundary. In so doing, we unite all of creation in recognition of HaShem. This is what it means to be a light unto the nations, an ohr lagoyim. When we fail to recognize who we truly are, (heaven forebid) then we fail in our task. (heaven forebid)
Only through acknowledging our deepest identity can we fulfill our role. Just like the story of Yonah, hiding wont help.