If religion is no longer the official and legal definition of Judaism, then being Jewish in Israel will be a distinction without a religious component. A strictly secular Jewish identity would be racial, and non-Jewish citizens of the State of Israel would be considered racially, as opposed to religiously, distinct. Without the religious cover, no one who is not of ethnic Jewish origin would be able to become "Jewish," and therefore, considered a separate race.
Monitor: Airstrikes hit Islamic State stronghold in Syria, killing at least 13 (Reuters)
from the article: Why Israel must become a secular state: a thought for Yom Kippur 5770