Thank you for asking a really great question.
Many of us have grown up in Church with a theology that says that Jesus is the ultimate sacrifice, putting an end to the sacrificial system. While it is built on truth, its conclusions about the sacrificial system being done away with clashes directly with the practice of the early disciples.
For example, after he wrote most of his NT letters, Paul the Apostle headed back to Jerusalem and happily agreed to pay the costs of four believers who were completing their vows. This included the believers offering a range of sacrifices in the Temple – costing in todays terms literally thousands of dollars. Neither these believers, nor Paul himself had an issue with performing this service. In Acts 24:17 Paul further explains that his purpose of going to Jerusalem in the first place was to give alms and offerings (in the language of the day, this clearly meant to sacrifice in the Temple). The book of Acts highlights further that the disciples met regularly in the Temple and were in high esteeem with all the people (which would have been hard to do if they suddenly rejected the God-given sacrificial system). Furthermore, Acts 6:7 describes that a number of priests joined the faith, and again there is no mention of them ceasing their work in the Temple because of their new found faith.
In essence the sacrifice of Jesus is on a higher level and represents a higher priesthood and does not do away with the Aaronic priesthood, it just serves a higher function. After all, the Aaronic priesthood was never able to take away sins in the first place. Furthermore, the Aaronic priesthood appears to be coming back into action in the Millennium according to the prophecies of Ezekiel.
It is true that the Aaronic sacrifices pointed to Jesus and gave much light on what He did for us. As such, these sacrifices would have taken on extra deep layers of meaning for these early disciples.
I hope this helps you, and let’s all continue to explore for ourselves what the Bible says of this topic.
I explore a similar topic in this video – ‘Can Christians support the rebuilding of the Temple?’:
Enoch Lavender was born in Australia, raised in Norway, spent time living in China and is now based in Melbourne, Australia. He has been studying Hebrew and the Jewish roots of our faith for the past decade, and has a keen interest in the Middle East from a Bible prophecy perspective.