Are Jews and Christians Mushrikeen?

As far as the Quran is concerned, one group from amongst the Jews at the time of Muhammad (pbuh) used to associate Ezra (pbuh) as son of God. Similarly, some sects of Christians also believed that Jesus (pbuh) was the son of God. Both these groups existed at the time of the revelation of Quran and Quran has also noted down these beliefs of theirs. However, Quran did not use the phrase 'mushrik' for the people of the Book despite this, rather this term, in the Quranic parlance, was used only for idolaters who associated others gods with God.

The reason, in my understanding, is the fact that by their own belief, both Jews and Christians subscribe to monotheistic faith. On the other hand, idolaters, or those whom the Quran has called Mushriks, accepted their belief to be polytheistic and believed that they were worshipping other gods than the God Himself. Needless to say, Islamic belief is that both Christians who take Jesus (pbuh) to be son of God and Jews who take Ezra (pbuh) to be son of God do associate partners with God.