Judaism is NOT a race. If it were it would be impossible to join it. Nor do all Jews "look alike". In the IDF, I have served with Russian blonde haired, blue eyed Jews, Yemenite olive skinned Jews, Ethiopian dark skinned Jews, and Jews from India who look almost Asian.
It is true Judaism is not just a religion, as my parents (who are not religious) can attest to, but Judaism is definitely not a "race" either.