Muslims do not reject the entire NT. They only reject what contradicts the Qur'an.
Many Muslims reject the Christ as "Son of God" because they have a misguided idea that Christians believe sex was involved with the conception of Jesus and nothing could be further from the truth. They misunderstand because the author of the Qur'an did not understand.
Jews reject the Christ because they do not believe He was the Christ -- they cite some of the prophecies of the Messiah that they believe Jesus did not fulfill.
Jews and Muslims are far from being on the same page.
Muslims believe Jesus was the Messiah, that He performed miracles, that He was born of a virgin and that someday He will return. Jews believe none of this.
Many of the Jews I know will not even discuss their Scriptures with Muslims because Muslims claim the Jews have changed their Scriptures.
For instance, Muslims tell me Jews deleted Ishmael's name from Genesis 22 and replaced it with Isaac's name.
Genesis 22:
2 Then God said, Take your son, your only son, whom you loveIsaacand go to the region of Moriah. Sacrifice him there as a burnt offering on a mountain I will show you.