There is no such thing as a Jewish race any more than there is an Arabic race, a white race, a Black race, there is only a human race.
Even though ethnically Jewish people tend to marry other ethnically Jewish people the evidence suggests that Jewish people in a given area are more closely related to non Jews there than they are to Jews from other parts of the world. This does not of cause prevent the Cohen line evidence being true it just means that the hole concept of race is pretty well meaningless.
When occasionally asked for my "Ethnicity" (a euphemism for race used in certain official forms here in the UK)I'm very tempted to put left-handed, which is as valid as any other characteristic,to base a "race" on.

All the best PP