Who is a Jew... According to Muslims?

In Islam, Ahlul al-Kitaab have a special, protected status. For example, a Muslim man may marry a Jewish or Christian woman. Because of this, it is relevant to determine who is a Jew or a Christian. It is easy to determine who is a Christian because anyone who professes a belief that Jesus is the divine son of God is accepted as a Christian. The same is not true, however, for Jews. It takes more to convert to Judaism (according to Jews) than simply professing a belief in Judaism. There is a whole long process, and the question of who is considered a Jew is controversial even among Jews themselves. For example, a [Reform](http://en.wikipedia.org/wiki/Reform_Judaism) conversion would not be accepted as valid by [Orthodox](http://en.wikipedia.org/wiki/Orthodox_Judaism) Jews. So according to the Orthodox Jews, someone who had a Reform Jewish conversion is not Jewish at all! So, for the purposes of the special protections granted to Jews and Christians, who is considered to be Jewish by Muslim doctrine? Is it anybody who professes belief in Judaism? Anyone who has had an Orthodox conversion? Maybe Reform conversions are ok? Perhaps only someone who is a descendent of the Jews who escaped Egypt and who has no conversions in his family is Jewish?