Judaism is a religion, not a race.
Judaism does not accept Jesus Christ as the promised Messiah. It is classified as on of the three “Abrahamic’ Religions alongside Christianity & Islam. The basic understanding of Judaism is that the Jews or those converted to the belief of Judaism still practice the old religion as outlined in what we know as the Old Testament. Other ancient writings that Judaism adheres to appear in what is know as the Talmud. The Talmud has two components; the Mishnah (Hebrew: משנה, c. year 200 CE), a written compendium of Rabbinic Judaism’s Oral Torah; and the Gemara (circa year 500 CE), an elucidation of the Mishnah and related Tannaitic writings that often ventures onto other subjects and expounds broadly on the Hebrew Bible.
From a Biblical New Testament viewpoint Judaism and Christianity are not synonymous because Judaism rejects Jesus Christ.
What does the Bible say?
1 John 2:22-23
22 Who is a liar but he that denieth that Jesus is the Christ? He is antichrist, that denieth the Father and the Son. 23 Whosoever denieth the Son, the same hath not the Father: (but) he that acknowledgeth the Son hath the Father also.
The above scripture clearly states that those who do not have the son (Jesus Christ), does not have the father (God). Some would have you believe that we are all worshipping the same God but based on the above scripture, we are clearly not.
Romans 2:28-29 King James Version
28 For he is not a Jew, which is one outwardly; neither is that circumcision, which is outward in the flesh:
29 But he is a Jew, which is one inwardly; and circumcision is that of the heart, in the spirit, and not in the letter; whose praise is not of men, but of God.