What part of Israel's past has influenced the country today?

Answer 1

Israel is a Jewish country, with a 75% Jewish population, of which a significant percentage is religious. Reform Judaism has made no inroads here.

Judaism is visible wherever you turn, with myriads of synagogues, thousands of institutions of Torah-learning, and public displays of Jewish occasions and concepts. To this day, the Hebrew Bible is held as our title-deed to the Holy Land. A certain amount of Torah-concepts are taught even in the non-religious schools and army.

Answer 2

Israeli law today is not based on the Torah; it's a blend of Ottoman laws, British laws, and others. However, Jewish laws do still have an effect:

• When Israel legislated a national day of rest for schools and businesses, it chose Saturday (the Jewish Sabbath), not Sunday. Sunday is a full workday in Israel.
  
• Many official and government functions are catered with kosher food. To purchase pork anywhere in Israel, or leavened bread on Passover, a person would have to make a serious search.
  
• Torah-holidays such as Passover and Sukkot are celebrated everywhere, not just in private. Hanukkah-menorahs are often displayed outdoors.
  
• Israeli coins have no human likenesses on them.
  
• The majority of marriages and funerals are at least nominally religious.
  
• Modern Israel gives legal status to the Hebrew calendar as well as the Gregorian one.
  

These are a few examples.

Link: More about modern Israel