This is simply not true
There cannot be 2 covenants ongoing at the one time. That is absurd! One terminated the other. There cannot be 2 competing priesthoods. One replaced the other.
The Law was to remain until all is fulfilled.
For truly I say to you, until heaven and earth pass away, not the smallest letter or stroke shall pass from the Law until all is fulfilled. (Matthew 5:18)
Hebrews 8:13: “In that he saith, A new covenant, he hath made the first old (palaioō, worn out, decayed, declared obsolete). Now that which decayeth (palaioō, worn out, decayed, declared obsolete) and waxeth old (gerasko) is ready to vanish away.”
Notice in the verse you quoted it said
"is ready to vanish away" meaning it had not occurred just yet.
The New Covenant didn't come into being instantly and the temple system was still in operation for Jewish believers from the period 30AD to 70AD (40 years). the Jews were born into the Law, therefore they had to continue to follow the Law. This did not apply to the gentiles as they were never under the Law.
God allowed the Jews who remained under the law time to repent, in hope that they would choose Christ.
The Lord is not slow about His promise, as some count slowness, but is patient toward you, not wishing for any to perish but for all to come to repentance. (2 Peter 3:9)
Just as the Israelites wandered in the wilderness for 40 years, so did those living in the 40 years from the time of the Resurrection to the destruction of the temple. Those who refused to believe in God’s Word failed to inherit His promise.
Jesus taught the continuation of offering of sacrifices at the temple.
Therefore if you are presenting your offering at the altar, and there remember that your brother has something against you, leave your offering there before the altar and go; first be reconciled to your brother, and then come and present your offering. (Matthew 5:23-24)
The Christian believers in Jerusalem were eagerly observing the law.
When we arrived at Jerusalem, the brothers received us warmly. The next day Paul and the rest of us went to see James, and all the elders were present. Paul greeted them and reported in detail what God had done among the Gentiles through his ministry. When they heard this, they praised God. Then they said to Paul: "You see, brother, how many thousands of Jews have believed, and all of them are zealous for the law. (Acts 21:17-20)
The ministry of Jesus and the twelve disciples was exclusively to the Jews.
"These twelve Jesus sent out with the following instructions: “Do not go among the Gentiles or enter any town of the Samaritans. Go rather to the lost sheep of Israel." (Matthew 10:5-6)
And this mission to the Jews continued for several years after the resurrection of Jesus as can be seen in the Book of Acts.
"Now those who had been scattered by the persecution that broke out when Stephen was killed traveled as far as Phoenicia, Cyprus and Antioch, spreading the word only among Jews." And Saul was consenting unto his death. And at that time there was a great persecution against the church which was at Jerusalem; and they were all scattered abroad throughout the regions of Judaea and Samaria, except the apostles. (Acts 8:1)
Paul received the mystery of salvation through grace after meeting the resurrected Jesus on the road to Damascus where the risen Lord appeared to him.
"As he neared Damascus on his journey, suddenly a light from heaven flashed around him. He fell to the ground and heard a voice say to him, “Saul, Saul, why do you persecute me?” “Who are you, Lord?” Saul asked. “I am Jesus, whom you are persecuting,” he replied. “Now get up and go into the city, and you will be told what you must do.” (Acts 9:3-6)
“Paul, an apostle—sent not from men nor by a man, but by Jesus Christ and God the Father, who raised him from the dead” (Galatians 1:1)
“I want you to know, brothers and sisters, that the gospel I preached is not of human origin. I did not receive it from any man, nor was I taught it; rather, I received it by revelation from Jesus Christ.” (Galatians 1:11-12)
The Law was still being taught by Jewish believers.
“Some men came down from Judea and began teaching the brethren, ‘Unless you are circumcised according to the custom of Moses, you cannot be saved.’” (Acts 15:1)
“Some of the sect of the Pharisees who had believed stood up, saying, “It is necessary to circumcise them and to direct them to observe the Law of Moses.” (Acts 15:5)
At first there was disagreement among the apostles between what Paul was teaching and what they were. This debate can be found in Acts 15 (The Council at Jerusalem), but in the end it was agreed that the Gentiles were free from the requirements of the of the Law for salvation. It was also decided that Paul and the others would minister to the gentiles and Peter and the apostles would continue their ministry among the Jews.
“The apostles and the elders came together to look into this matter. After there had been much debate, Peter stood up and said to them, ‘Brethren, you know that in the early days God made a choice among you, that by my mouth the Gentiles would hear the word of the gospel and believe. And God, who knows the heart, testified to them giving them the Holy Spirit, just as He also did to us; and He made no distinction between us and them, cleansing their hearts by faith. Now therefore why do you put God to the test by placing upon the neck of the disciples a yoke which neither our fathers nor we have been able to bear? But we believe that we are saved through the grace of the Lord Jesus, in the same way as they also are.’” (Acts 15:6-11)
The council came to agreement that both Jews and Gentiles are saved through the same process, through the grace of God, and Paul refers back to this debate in Galatians.
“On the contrary, they recognized that I had been entrusted with the task of preaching the gospel to the uncircumcised (gentiles), just as Peter had been to the circumcised(Jews). For God, who was at work in Peter as an apostle to the circumcised, was also at work in me as an apostle to the Gentiles. James, Cephas and John, those esteemed as pillars, gave me and Barnabas the right hand of fellowship when they recognized the grace given to me. They agreed that we should go to the Gentiles, and they to the circumcised.” (Galatians 2:7-9)
As can be seen there was a gradual transformation between the New and the Old. The Old Covenant and New ran parallel to one another until the temple was destroyed.
When He said, “A new covenant,” He has made the first obsolete. But whatever is becoming obsolete and growing old is ready to disappear. (
Hebrews 8:13)
The temple, the sacrificial system, and the priesthood, were done away in 70AD and the Jews could no longer look to them for redemption or atonement. From that day forward forgiveness and mercy could only be found through Jesus Christ and His work on the cross alone.
All authorities concur in the declaration that “when all these things should have been done”, ‘The End’ should come: that “the mystery of God should be finished as he had declared to His servants the prophets“: it should be completed: time should now be no more: the End of all things (so foretold) should be at hand, and be fully brought to pass: in these days should be fulfilled all that had been spoken of Christ (and of His church) by the prophets: or, in other words, when the gospel should have been preached in all the world for a testimony to all nations, and the power of the Holy People be scattered (abroad), then should the End come, then should all these things be finished. I need now only say, all these things have been done: the old and elementary system passed away with a great noise; all these predicted empires have actually fallen, and the new kingdom, the new heaven and earth, the new Jerusalem–all of which were to descend from God, to be formed by His power, have been realised on earth; all these things have been done in the sight of all the nations; God’s holy arm has been made bare in their sight: His judgments have prevailed, and they remain for an everlasting testimony to the whole world. His kingdom has come, as it was foretold it should, and His will has, so far, been done; His purposes have been finished. -- Eusebius