To answer this question we should first examine the context of the use of the term for their predecessors. What is a Jew? Taking this term at face value leads straight to big problems. There were historically, in the time of Yeshua/Isa three known, clearly identifiable groups of Jews, with a fourth he created. In the time of the Qur'anic revelation there were likely only two different groups of Jews. One being that of Pharisaic Judaism, the other being but a few surviving descendants of the Aaronic line, Tsadokim. Yahovah/Allah elected to use a generic term to test and limit the understanding of scholars. Since this time the Islamic world has had to come to terms with the existence of the Karaite movement in Judaism. Some Karaites are Tsadokim, a remnant of the Sadducees that bibles mention. Karaites likely reflect the theology of the early Tsadokim most closely. Of course there were differing perspective in Pharisaic Judaism, like the historic schools of Hillel versus Shammai. The Qur'an acknowledges differing sects of the three base monotheist religions. If the term Jew, being a noble title in context, may be used generically, then why not that for the Nasara?
Not being an Arabic speaker, nor having close links to Islam I was shocked to see how a couple of things are being translated into English from the Qur'an. No way can the term nasara be translated as Christian. From the information presented here it seems as though the term in question is being used as a pun. The word can mean supporter in a Qur'anic context or Netzerim by historic usage. The term Netzerim is biblical, and noble in context, but just as in Judaism, things changed. The first Jew was Yerimahyahu/Jeremiah (Mordechai Schreiber - The Man Who Knew God). The original Netzer was Yeshua ben Miriam. The term Netzer is different to Netzert/Nazareth. A netzer is literally an offshoot, a reference to Yeshua's unique genealogy. So the Netzerim are followers of the offshoot. The debased religion that is christianity is an offshoot of the Netzerim, and the vine planted outside of the Creator shall be uprooted and destroyed (Thomas 40).