Customary Jewish popular thinking about Christianity is out of touch and deeply misinformed. In contrast, leading conservative Christian and Jewish intellectuals today regard each others' faith with deep appreciation. Commentary regularly demonstrates sympathy for Christianity, and First Things similarly demonstrates sympathy for Judaism.
This is the chr*stian position. It is not the Jewish position, since it assumes the inspiration of the "new testament," which Jews and Noachides do not.
If we go back to the time of the flood, when all the wicked perished and only the family of Noah survived, all the people that survived at that time were gentiles. The covenant made at that time, in Genesis 9, is known as the Noahic Covenant, and was for all people.
Later at Sinai another covenant was made, this time with those that became the Israelites. This covenant consisted of the same things as the Noahic covenant, but it had additional commandments as well. These additional commandments pertained to the Israelites because they were to be a light unto the nations. They were to be an example to the gentiles. The Israelites were to be a Holy nation. The extra commandments pertained to dietary guidelines for purity, they also contained commandments for their 'priesthood', and Sabbath keeping.
Now, back to Noah and his family. As people dispersed, they took the Noahic Covenant with them. This is why we see so many similarities between so many religions of the world. There are differences too. These differences are what we call today 'traditions of man'. Remove these differences, and focus on the similarities and you find 3 things.
1. Belief in G-d
2. Instructions in moral conduct (we know them as the 10 commandments, but other religions call them other things, such as the 10 fold path, the negative confessions, the precious garland, the 10 charges, etc.)
3. The Golden rule, or Royal rule. We know this as 'do unto others'.
Try your best to treat others as you would wish to be treated yourself, and you will find that this is the shortest way to benevolence. (Confucianism - Mencius VII.A.4 )Whatever you wish that men would do to you, do so to them. (Christianity - Bible, Matthew 7:12)
Tsekung asked, "Is there one word that can serve as a principle of conduct for life?" Confucius replied, "It is the word shu--reciprocity: Do not do to others what you do not want them to do to you." (Confucianism - Analects 15.23)
Confucious predates Yehoshua/Joshua (Jesus) by about 500 years.
As you can see, 'universality' was already set into place long before christianity came along. One faith, one family.