In demanding the right for their rabbis to convert non-Jews in Israel, the Reform and Conservative movements are not asking for a change in the law but rather for what they believe to be the correct interpretation of existing law - namely the Law of Return.
According to Article 4B, which was added to the original legislation in 1970, "For the purposes of this Law, 'Jew' means a person who was born of a Jewish mother or has become converted to Judaism, and who is not a member of another religion."
From a strictly legal point of view, the Reform and Conservative movements argue that the definition of being a Jew does not specify how the non-Jew has been converted, including by what religious stream.
From a social and ethical point of view, the movements argue that no specific stream of Judaism should have a monopoly on conversions and that each person has the right to convert in accordance with the religious ideology that best represents his own beliefs.
The Orthodox establishment in Israel does not recognize the Reform and Conservative movements on the grounds that they allegedly violate religious law (halacha.) Therefore, they are not Jewish in any meaningful sense of the word and have no right to preside over any of the religious ceremonies that the Jewish faith calls for.
So far, the Reform and Conservative movements have not challenged the Orthodox monopoly on conducting marriages or granting divorces, because these prerogatives of the rabbinical courts are recognized by law.
But the Law of Return is a secular law which does not deal with the merits of different religious streams or definitions of Judaism and does not provide any operative details about what it means by "has become converted." Therefore, unless the Knesset were to change the Law of Return or pass another law overriding it, the current legal state of affairs does not prefer one type of conversion over another. Therefore, argue the Reform and Conservative movements, the government has no choice but to recognize as Jews in accordance with the Law of Return "anyone who has converted to Judaism."