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This would be at odds with polls over the years which show that upwards of 70% of Israel's Jews fast on Yom Kippur, celebrate the holidays, around half observing Kashrut and Shabbos. But perhaps not in complete compliance. To an Israeli the term religious would likely connote what is referred to by non-Israelis as ultra Orthodox or Orthodox. And 20% of the population is Muslim. How did they answer. Was their an implication in the question that the religion was Judaism. It's hard to think many Muslims acknowledged to a poll they don't believe in their faith.
http://www.chabad.org/library/article_cdo/aid/45132/jewish/What-Makes-a-Jew-Jewish.htm
...The Torah itself proclaims (Leviticus 16:16) that G-d “dwells amongst them in the midst of their impurities” — that His relationship with His people remains unaffected regardless of their behavior. In the words of the Talmud (Sanhedrin 44a), “A Jew, although he has transgressed, is a Jew.”
According to Torah law, a person’s Jewishness is not a matter of life-style or self-perception: one may be totally unaware of one’s Jewishness and still be a Jew, or one may consider himself Jewish and observe all the precepts of the Torah and still not be a Jew.
In other words, it is the relationship between the Jew and his Creator that defines his Jewishness — not his acknowledgment of this relationship or his actualization of it in his daily life. It is not the observance of Torah’s mitzvot (Divine “commandments”) that makes him a Jew, but the commitment that the mitzvot represent...