The Karaites disobey Deuteronomy 17:8-13, which gives authority to the religious leaders to interpret the law.
The religious leaders were not given power under the Torah to add or subtract anything to the law. And in the Torah, God laid out the judgments that the judges were to give in various cases, so judges were not left with freedom of interpretation. In case of doubt, the High Priest was given the Urim and Thummim as direct oracles by which God could always be consulted directly.
The cardinal difference between Karaites and traditional Judaism is that the Karaites accept the Torah as being God's Law (as do all Jews - even the Reform, who honor it in the breach - but, like Samaritans, they reject the rest of the Jewish writings, the rest of the Old Testament, as being authoritative. God gave the law to Moses and the Israelites, and he explictly bound them in that law to add nothing, and to subtract nothing.
Exercising "interpretive authority", the Priests and Levites added much, and subtracted much. The Karaites reject all of that. Jesus criticized it also, pointing out several places where the Jewish religious authorities, in adding to the law, nullified the actual law.
Of course Jesus went further than that. God gave the law of divorce to Moses. But Jesus nullified it...thereby creating a conflict with his own words in another place, where he said that not a penstroke nor an iota of the law would pass until the end of the world.
The two statements cannot be perfectly reconciled, and so looking at what Jesus said and did, one must realize that Jesus did strike away several laws that were not simply traditions of the rabbis but were part of the written Torah, that the world hasn't ended yet, and therefore that his statement that not a penstroke or iota would pass from the law is a rhetorical exaggeration, just like his statement that the mustard seed is the smallest seed. It isn't. It was the smallest seed that farmers in Israel were accustomed to, and that was good enough for his purposes.
The tension between the Law and Jesus' teachings is present even within Jesus' teachings, and within Christianity itself we can see the echoes of the schools of Hillel and of Shammai, in that most Christians think Jesus changed the law through the power of grace and the authority of divine Sonship, but a minority think that he did not and could not, and that all of the Jewish strictures apply to Christians also, and will until the end of time.
We all have an opinion on the matter, and universal agreement isn't possible because what Jesus said in one place contradicts what he actually did in several places.
My own solution is to note that he was talking to Jews, that only Jews were ever bound under the Jewish law, so that whether or not the Jewish law remains perfectly intact, or was changed by Jesus, or ceased to exist with the destruction of the Temple, which marked the end of that "kosmos" doesn't make any different to a Gentile like me. Neither me nor any of my people were ever Jews, or subject to the Jewish law, and so it does not matter at all from my perspective whether the Law is gone or still in force, because that Law didn't apply to Gentiles before Moses, in the time of Moses, or since Moses. It was a law for Israelites only.
The Law of Jesus is the law for the rest of us, and that is much simpler and more direct (and less known, because people are so fascinated by the Jewish law...because Jesus' audience was Jewish and THEY were fascinated by that Law) than the Law of Moses.
The Law that applies to ME is the Law of YHWH at creation, of Noah after the Flood, and of Jesus.
The kosher laws of the Jews are interesting, but they were never laws for me or my ancestors going back to the beginning of time. So it's a purely academic exercise, and not something to get exercised with one another over.
Oysters in the Eastern Med are squidgy. I'm pretty sure that if the Promised Land were in Norway, YHWH would not have made shellfish "unclean", because they're not unclean THERE. They sure are in the land that God gave to the Hebrews though. Hebrews were never meant to be in Norway.