According to classical Judaism, someone can be a Jew through matrilineal descent or Jewish legal conversion. Thus, according to this view, an individual’s religious beliefs are largely independent of his/her status as a Jew.
In other words, according to traditional Judaism, someone can believe in Judaism but not be a Jew, and vice-versa. Classical Jewish law maintains heavier requirements of observence for someone who is technically a Jew. Consequently, conversion is usually discouraged unless the potential convert is dedicated to following the strict legal code required for Jews.