Jew is historically associated with anyone from Judea (Israel). Judeans (jew) when written in arabic / Hebrew becomes Yehudi. Thus a jew must not follow Judaism to become a jew.
Majority of jews in Israel are atheists or secular. Only a minority is practicing jews (followers of Judaism)
@Natan @500 is my definition of a jew correct?
The term "Jew", comes from Judah (Yehuda), fourth son of Jacob, who is regarded as the ancestor of Tribe of Judah.
Tribes eventually became one Kingdom of Israel, but that vast
united kingdom didn't last long and split into northern Kingdom of Israel, and southern Kingdom of Judah. The heart of the southern kingdom was Judea - Hebron, Bethlehem, and, of course, the capital Jerusalem.
Northern Kingdom of Israel was defeated by Assyrian Empire, and its tribes were taken to Assyria and lost.
Southern Kingdom of Judah, consisting mainly of Tribe of Judah and parts of tribes of Benjamin and Simeon, remained. The people of Kingdom of Judah became known as Yehudim / Yahudi / Jews.
So it was Judah, Tribe of Judah, Kingdom of Judah, who gave the name "Judea" to modern day Judea, and eventually the name "Jews" to the people.
Jewish tradition says that a Jew is someone who's mother was Jew. But throughout the history people also used to convert to Judaism and within one generation became Jews.
For almost 2000 years only followers of Judaism were considered Jews by themselves and by the surrounding nations. But in late 19th century and in 20th century, of course, situation changed. Some Jews began considering themselves Jews without following Judaism, and people of Jewish origin who were not following Judaism at all were prosecuted by surrounding nations equally to those who were strict believers.
So, now its is complicated. Modern Jews are either born-Jews, or converted-to-Judaism. Born-Jews are either followers of Judaism or not, but converted-to-Judaism obviously remain as followers.
In modern Israel some 40% of the Jews are secular atheists, another 50% are followers of Judaism (any kind from almost secular to almost ultra-orthodox), and another 10% are strictest ultra-orthodox.