Being Jewish without practicing Judaism

Is it possible to be Jewish if you don't believe in Judaism or its Holy books? If so what exactly does that mean to be Jewish but not religiously Jewish?

Shalom,

A person born to a Jewish mother remains Jewish forever, even without believing in God and fulfilling His commandments. Such a person is called a secular Jew, i.e. a Jew who is not religious.

However, if a Non-Jew wants to convert to Judaism, he must accept upon himself to observe of the commandments. His failure to do so invalidates his conversion, and he does not become Jewish.