I am not sure what evidence you are using to show that Christians were still performing sacrifices in Jerusalem after Christ died. Can you inform me of the evidence that this is the case? You say that it is an “historical fact… that the followers of Jesus Christ went on participating in the sacrificial system in the temple.” I have never seen any evidence that Christians were still performing actual sacrifices as priests in the temple. Perhaps you can tell me the source of this “historical fact.” I am not saying it is not true, but, if I am going to respond to your question, I need to see this evidence. To be honest, I am rather skeptical that there is such evidence, and I am somewhat skeptical that Christians were actually performing such sacrifices. The Jewish believers were still celebrating Jewish festivals such as Passover, Tabernacles, and Yom Kippur. They continued Jewish practices, including eating kosher and observing Sabbath, but I believe this claim that they were making sacrifices in the Temple is not supported by any evidence. Paul also observed many Jewish traditions after he became a Christian, but he surely did not continue to make animal sacrifices. I, myself, have taken part in a Seder service. Paul told us that taking part in one of these Jewish observances is neither required, not prohibited (Colossians 2:16-17).
I am not sure it would be “wrong” or “sinful” to perform an animal sacrifice as a Christian, but it would be confusing for a follower of Jesus to do so. I can see why you imply that this would be problematic. But, like I said, I believe that there is no evidence that they were doing so. Who informed you that this is an “historical fact.” I believe that they are trying to make trouble, and that this is misinformation.
Here is what I can say with 100% certainty: The believers in Christ were well aware that he was crucified, that he was raised from the dead, and that this provided for the purification from sins. There was no time when Christians were not aware of the death of Christ. The Lord’s Supper, as a remembrance of Christ’s sacrificial death, was present in all Christian worship from the earliest possible date. This is what the evidence tells us. Acts 2:42-47 tells us that they were taking part in the Communion from the very beginning. Paul’s letter to the Corinthians, from about AD 56 is further proof that this was always part of Christian worship.
John Oakes