The definition of race as it has always been applied to Jews is the classic anthropological definition, in which race is characterized by skin color and other biological attributes that are shared by a group. Judaism is strictly a religion and is not rooted in biology. You or I could've been born racially Semitic, but no one can be born racially Jewish. It isn't possible. Judaism, like many other religions, is comprised of many races of people and accepts converts. And converts are not chosen by race or any other hereditary or ethnic factors.
Western-backed Syrian rebels say kill foreign Islamic State (Reuters)
from the article: Is Judaism a race? Ask Israelis