There is a common idea that Christianity is simply and extension of Judaism, that it takes the religion of the Old Testament and simply adds a Messiah to it. In this view Judaism should be regarded as a completely legitimate belief equivalent to Christianity. Jews don’t extend the same courtesy, but that’s another story.
This creates various problems. Some reject Christianity out of hand as a “Jewish” religion. Many Christians look at the Old Testament as essentially a historical oddity, superceded by the teachings of Jesus. Even those who don’t take this view explicitly take the idea of a “law” as sort of obsessive and pointless.
Some Jews get extremely bitter with the idea that Christianity “supercedes” Judaism. The idea that Christianity might actually replace Judaism is very toxic especially after World War II. So the idea that Christianity is just an extension of Judaism, closely related and not hostile, has been the official line of many Christians looking to avoid controversy. This last part directly contradicts what Jesus himself said, but as long as people are avoiding controversy nobody looks at things too closely.
This view of things doesn’t take into account the social evolution of the people described in the Old Testament, who to avoid confusion I will call the Hebrews. The Old Testament is largely the story of the Hebrews, from their establishment as the descendents of Abraham through Jacob through their initial wanderings around the Middle East and their settling in Canaan. They receive God’s blessing, then a legal code. They fought various hostile neighbors, established a temple in the city of Jerusalem, and yet repeatedly fall back into idolatry and other prohibited behavior.
The Hebrews were an agricultural people, but a certain few were designated to have religious duties only, first wherever the Ark of the Covenant was kept, then later at the temple in Jerusalem. The farming and herding Hebrews were required to make contributions for the support of the priest class and for general welfare. The religious code required various sacrifices either as offerings of agricultural products or in propitiation of offenses.
A system like this has potential for abuse. The priests can extort offerings out of people, and people can buy their way out of trouble. One of the last chronological books of the OT is Isaiah, which is harshly critical of the system of temple worship. Isaiah posits a universal form of worship for all people without sacrifices.
Nevertheless, 500 years later the temple was still operating with the same sacrificial system. The temple was big business. Rural Hebrews had to travel to Jerusalem and stay there, benefiting innkeepers. They had to buy animals to sacrifice, and if they had foreign coins, they had to exchange them for temple currency, because sacrificing an animal purchased with Roman money would be unacceptable- this is the explanation for why there were money changers in the temple courtyard.
Rural Hebrews became pretty bitter about this system. There was a class of urban Hebrews that profited and became rich out of their need to maintain worship and good religious status. If you were poor, you might fall out of religious favor and acceptable social status altogether. Beyond the Hebrews making money of religion, there was a class of religious scholars that obsessively studied the scriptures and a whole new set of complicated and difficult to follow rules.
The rebellion of John the Baptist and Jesus against this system is laid out in the New Testament. Beyond the ego bruising of having some hicks from the sticks challenge the authority of the temple priesthood, the new form of worship threatened the incomes of a lot of people in Jerusalem, and this was another motivation for their killings. In the end, it made no difference, because the temple was destroyed by the Romans after a Hebrew revolt and temple worship came to an end.
The Romans expelled the Hebrews they didn’t kill from Jerusalem. Many urban Hebrews had already moved to other cities in the empire and just studied or read the scripture in synagogues. Some years after the destruction of the temple the urban Hebrews asked the Romans for permission to establish schools for the study and analysis of the scriptures, and it was granted. Some remained Middle Eastern and are refered to as Sephardic, others moved around Europe and mixed with other peoples. These people are who are now refered to as Jews, and the post-temple form of religion they developed is called Judaism. Jews gained control of Jerusalem after World War II, but while they pray at the remains of the temple, they have never attempted to rebuild it, have no temple priesthood and don’t offer sacrifices.
Christianity can’t be said to come from Judaism, to take the pro-Judaic view, nor can it be said to replace it, to take the anti-Judaic view. Both Christianity and Judaism come from the crisis of the Hebrew nation at the beginning of the first millennium. Jews can’t claim that their belief predates Christianity, actually rabbinical Judaism got started after Christianity. Jews also can’t claim to be the descendents of the Hebrews of the Old Testament- or they can only claim to be partially descended from a small number of them, as most people then were not city dwellers and they mixed with other groups in their migrations.
The idea that Christianity comes from Judaism is problematic for all Christians. Christians hostile to Jews have to wrestle with the idea that their belief comes from theirs- although I think I have shown the two are only incidentally related. Christians friendly to Jews still think of the Old Testament as something inherently foreign and irrelevant. Christian Identity attempts to deal with this by saying that Jews are not actually the descendents of the Hebrews, but Europeans are.
The legalistic belief system of the urban Hebrews was bitterly, harshly criticized by Jesus. But he did not, regardless of what anyone says, reject or supercede the law at all. To me, both ideas- that the law must be obsessively followed, or that it is irrelevant- miss the point. Overanalyzing a law tends to lead to finding ways to evade it. Discounting it entirely, or depending on something as vague as “love”, leaves the door open for a lot of rationalizing of bad behavior. I think the answer is in the Old Testament itself. In the Psalms, David talks about the importance of studying the law, and its wisdom and beauty, but also that no one can know all his faults and that we are dependent on God for holiness.