The Baal Shem Tov once went to the mikveh in a place that was populated by non-Jewish people. On his way back, after toiveling, he was concerned that a goy may touch him. While he was walking, he overheard one gentile tell another, “Be careful not to touch this contaminated Jew.”
His grandson, the author of Degel Machaneh Ephraim explained that this is the meaning of the possuk, “Hein am l’vadad yishkon” – “They are a nation that dwells apart.” The Yidden do not mingle with the goyim because (as that possuk continues), “uvagoyim lo yischashov” - “they are not counted among the nations,” that is to say, the Yidden are not esteemed in the eyes of the goyim. And paradoxically, this is for the Yid’s benefit!
On numerous occasions the Rebbe emphasized that standing apart from the goyim in all areas of conduct will not cause the goyim to dislike the Yidden (as some Yidden over history had believed); on the contrary, it will elicit their respect and admiration, seeing how the Yidden live distinct and true to their tradition.