Disseminating Torah-true Judaism, Chasidic philosophy, and the Noahide Code as widely as possible, without being adversely affected, is not a goal that the Rebbe reserved only for Chabad Chassidim. Rather, he “paved the way” for all Jews to do so. However, this ability is specifically attained through connecting to Chabad Shluchim and Chabad Chassidim in general, the “conduits” through which all Jews connect to the Rebbe:
My father-in-law, the [Previous Lubavitcher] Rebbe, paved the way for all his students and emissaries who follow in his ways, and via them, [these ways reach] to all the Jewish people. He enabled them to occupy themselves with disseminating Torah and Judaism, and spreading the wellsprings of Chasidic philosophy in every place and circumstance—even in “Egypt,” i.e., a place furthermost from G–dliness.
They can perform this in a way that not only does their presence in the “outside” (Egypt) not detract from their attachment to G–d, but on the contrary: They can influence the entire “land of Egypt,” fulfilling the imperative upon Jews “to compel all the world’s inhabitants to undertake the laws commanded to Noah’s descendants ... because the Holy One, blessed be He, commanded them in the Torah and informed us via Moses, our teacher [that these laws are binding on gentiles],” as Maimonides rules clearly.
Likkutei Sichos, Vol. 30, p. 228.
Moreover, not only will one not be harmed by this experience, but he will be elevated to an incomparably higher level:
Even if it sometimes appears initially that this is a mission of Elokim—in a manner of judgment and concealment, especially if concealments arise that cause pain and anguish—from Joseph we receive the power to reveal G–dliness even in the place to which we were assigned, and even to reach (via this descent) a tremendous, lofty level, as symbolized in the verse [concerning the Biblical Joseph], “G–d will add for me another son,” to the point that one reaches an incomparably more sublime level.
By increasing with even greater vigor the service of “Joseph”—disseminating Torah and Judaism and the wellsprings of Chasidic philosophy outward, until the level furthermost from G–dliness, we hasten the true and complete redemption by our righteous Messiah, who will rebuild the Holy Temple in its place, gather the Jewish exiles, and rectify the entire world to serve G–d together, speedily in our days.
 Mishneh Torah, Laws of Kings, 8:10-11.
 This name of G-d represents the divine attribute of strictness.
 This is a reference to the Previous Lubavitcher Rebbe, whose first name was Yosef.
 Bereishis 30:24.
May we all merit to fulfill this task.