Jewish people across the world tended to keep to themselves and speak unique languages before the 19th/20th century.

Most North American Jews are descended from Ashkenazi (eastern European) Jews. These guys lived primarily in what is now Poland, Germany and Russia. They spoke their own language (Yiddish) and lived apart in segregated rural communities or urban ghettos. They also faced brutal discrimination at the hands of all their neighbors that culminated in the Holocaust.

The language is enough to qualify these guys as an ethnic group, and when you consider the fact they were brutally massacred by Poles, Germans and Russians it's not surprising that they want to be recognized as a separate people.

Non-Ashkenazi Jews in America, who wouldn't have traditionally spoken Yiddish but would have spoken languages like ladino (Jewish Spanish) or Jewish Arabic, generally assimilated with the larger Ashkenazi community. This was facilitated by the old testament teaching all Jews are one tribe, as well the rise of Hebrew over Yiddish in the 20th century.

Strictly speaking, however Judaism is not an ethnic identity, but rather a group of ethnicities united by faith. I have heard non-academic accounts of there being ethnic tension/divides in Israel between the descendants of different Jewish groups.