Describe the religious landscape into which Christianity first appeared. Identify the beliefs and practices that distinguished it from Judaism

The rise of Christianity needs to be understood against the background of two contradictory world views: Judaism and paganism. To some extent, Christianity achieved its rapid success by synthesising the two rival outlooks to create a completely new religion, albeit one that still retained elements of its more ancient antecedents.
Initially, Christianity was seen as an heretical cult within Judaism. Jesus was a Jew, along with his disciples. And all of them openly identified as such. Jesus preached only to other Jews as Christianity in its earliest guise was an attempt at perfecting Judaism rather than abandoning it altogether. Early Christians still worshipped and practised within the boundaries of the Mosaic Law.
But tensions soon developed in what eventually became a full-blown sectarian split within Judaism. The main source of tension was that the followers of Jesus regarded him as the Messiah, as prophesied in the Hebrew scriptures. But the traditional understanding of the Messiah in Judaism was of a worldly savior, one who would come to free the Jewish people and restore their earthly kingdom to its former glory. The Christian Messiah, on the other hand, the Christ, was the son of God, and had been sent to earth to save all humankind. His kingdom was not of this earth; and his message was universal as opposed to being aimed solely at one particular group, as Jewish Messianism was.
It was this tension between the universal and the particular that ultimately led to the final split within Judaism and established Christianity as a separate and distinct religion in its own right. In this regard, Paul is a hugely significant figure. He spread the Christian message to Gentiles living beyond the Hebraic world, in cultures and lands permeated with the spirit of paganism.
In order for Paul to be successful in his evangelizing mission it became necessary for him to accommodate the still Jewish sect of early Christianity to the pagan worldview. For instance, Paul insisted that it wasn't necessary to be a Jew before one became a Christian. This helped to get round thorny problems relating to religious observance and practice such as the Eucharist. Previously, Jewish Christians were reluctant to share in the eucharistic meal with Gentiles, but Paul recognized that this practice could not be allowed to continue if Christianity were to make good on the universality of its message.
The practice of circumcision was also highly contentious. In Galatians, Paul explicitly states that circumcision is unnecessary for salvation:
Gal. 5:6: "For in Christ Jesus neither circumcision nor uncircumcision avails anything, but faith working through love."
Gal. 6:15: "For in Christ Jesus neither circumcision nor uncircumcision avails anything, but a new creation."
Here we see the development of a growing gap between the legalism of Judaism and the spirit of Christianity. In substantial terms, once early Christians had ceased carrying out Jewish practices it was no longer a Jewish sect. Formally, however, it wasn't until well into the 1st century CE that it became possible to speak of the existence of two separate religions, Judaism and Christianity.
 
https://www.biblicalarchaeology.org/daily/biblical-topics/new-testament/the-origin-of-christianity/