Yes, but these provisions are themselves subject to varying degrees of interpretation. In Israel conversion and marriage are controlled by the Orthodox. Sharon's remarks, nor any Israeli law, can change the Jewish laws. But Sharon can change the Israeli governments definition of who is a Jew. And he can appeal to the Beit Din (Religious court) to reexamine the issues of conversion.
At one time (a long time ago) it mattered not whether your mother of father was a Jew -- either would do. Now it is matrilinial.
To become a Jew in Israel, one has to undergo a rigorous lifestyle change, and depending on which sect you choose so goes the type of change. To become a Jew in the USA, depending on which sect and which branch (orthodox, conservative or reform), you may not have to change your life much.
But the Orthodox will not accept a reform or conservative conversion. The result is a lot of confused people, a lot of unhappy people, and a lot of people who want to be Jews but do not accept the Orthodox interpretation of Halacha.
As in the days of yore, there were the Pharisees, Saducees and other sects of Jews. Each sect adopted different interpretations of Jewish law. There needs to be more unanimity.
Before I ramble too much, there is a question of priority. If the Orthodox believe that having more Jews is a priority, they will change their rulings to permit easier conversion, and hope that those who convert will slowly come closer to living a Torah life. The way it stands now, they want proof that you will live a Torah (as defined by them) life BEFORE you will convert. And in many respects it is a double standard, because even the Orthodox recognize the principle that no Jew is perfect, and that one of the purposes in life for a Jew is to spend the life becoming a better Jew one step at a time.