I don't see any scripture in either testament that says we are to adhere to the "synagogue culturally". In fact, I don't even see where the Old Covenant speaks of meeting in a synagogue at all. Likewise, the New Testament doesn't speak of a "church building" in which Christians meet. One possible exception is "the school of Tyrannus" in Acts 19:9, in which Christians were taught temporarily for two years. But most assemblies met in homes, which is the most practical, because not everyone could travel the distance to that particular school
The Israelites did some soul search after the destruction of the 1st Temple about what went wrong and the problem was that they didn't know the Torah, so the synagogue system was developed as the solution to the problem.
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Jesus said that He would build His church, but He never directed anyone to build a material building for assemblies.
The Greek word "ekklesia" is translated as "church" and it is used many times in the Septuagint to refer to Israel in the wilderness
Nor does the scripture tell us that when we are born again, we will become part of one of the twelve tribes of Israel. What a bizarre belief that is.
A child of someone is a person who is in their likeness through embodying their character traits such as with John 8:39 where Jesus said that if they were children of Abraham then they would be doers of the same works as him. This is why those who are not doers of righteous works in obedience to the Torah are not children of God (1 John 3:4-10) and why Paul contrasted those who walk in the Spirit with those who have minds set on the flesh who are enemies of God who refuse to submit to the Torah (Romans 8:4-7). The Son is the radiance of God's glory and the exact likeness of His character (Hebrews 1:3), which he embodied through his works by setting a sinless example for us to follow of how to walk in obedience to the Torah, so that is what it means for Jesus to be the Son of God and what it means for us to be born again as children of God when we are partaking in the divine nature through following his example.
In Ephesians 2:12-19, Gentiles were at one time separated from Christ, alienated from Israel and strangers to the covenants of promise, having no hope and without God in this world, which is in accordance with Gentiles at one time not being doers of the Torah, but through faith in Christ all of that is no longer true in that Gentiles are no longer strangers or aliens but are fellow citizens of Israel along with the household of God, becoming born again goes hand in hand with becoming joined with Israel.
Paul said, "Be imitators of Me, just as I also am of Christ." 1 Corinthians 11:1
Did Paul keep the Law of Moses? No, not generally. He would keep some of it at times, so as to not offend the Jews that he was trying to win for Christ. But he said, " ... though not being myself under the Law; " 1 Corinthians 9:20 But when he was around Gentiles, he would zealously avoid keeping the Law, so they would not think that being a Christian meant keeping the Law.
So if he was imitating Christ, we know that Christ Himself also did not generally keep the Law, except occasionally for the same reason that Paul did.
Sin is the transgression of the Torah (1 John 3:4), so the fact that Jesus was sinless means that he set a perfect example for us to follow of how to be a doer of God's character traits in obedience to the Torah and that Paul being an imitator of him also means that he was a doer of God's character traits in obedience to the Torah and that we should be imitators of them. In Acts 24:14, Paul said that according to The Way, which they call a sect, he continued to worship the God of their fathers, believing everything laid down by the Torah and written in the Prophets, so Paul certainly walked in God's way in obedience to the Torah. In 1 Corinthians 9:21, Paul used a parallel statement to equate not being outside the Torah with being under the Law of Christ.
But we know that the Law of Moses became obsolete, according to Hebrews 8:13. When did that happen? Well, God Himself started the ball rolling when He tore the temple veil in two, when Jesus said, "It is finished." About forty years later, in 70 A.D., He finished the job, by having Titus, the Roman general completely destroy the temple and Jerusalem.
God's character traits are eternal, therefore any instructions that God has given for how to be a doer of His character traits are also eternal and cumulatively valid even for those who are not in a covenant relationship with Him. For example, God's righteousness is eternal (Psalm 119:142), therefore all of God's righteous laws are also eternal (Psalm 119:160). For instance, it was in accordance with God's righteousness to be a doer of charity before God made any covenants with man, so there is nothing about the Mosaic Covenant becoming obsolete that means that it is no longer in accordance with God's righteousness to be a doer of charity. Sin is what is contrary to God's character traits and sin was in the world before the Torah was given (Romans 5:13), so there were no actions that became righteous or unrighteous when the Torah was given, but rather it revealed what has always been and will always be the one to do that.
New covenants do not nullify the promises of covenants that have already been ratified, so God's covenants are eternally and cumulatively valid. The Mosaic Covenant is eternal (Exodus 31:14-17, Leviticus 24:8), so the only way that it can be replaced by the New Covenant is if it is cumulative with it. One thing can only make another thing obsolete to the extent that it has cumulative functionality, so a computer makes a typewriter obsolete but does not make a plow obsolete, which means that if the New Covenant involved doing something different that was not cumulative with the Mosaic Covenant, then it could not make it obsolete. So the New Covenant still involves following the Torah (Hebrews 8:10) plus it is cumulatively based on better promises and has a superior mediator (Hebrews 8:6). The fault that God found with the Mosaic Covenant was not with His righteousness or with His righteous laws, but rather he found fault with the people for not continuing in their covenant (Hebrews 8:7-9), so the solution to the problem was not for God to do away with His righteousness or righteous laws, but to do away with what was hindering us from obeying them. This is why the New Covenant involves God sending His Son to free us from sin so that we might be free to meet the righteous requirement of the Torah (Romans 8:3-4), God taking away our hearts of stone, giving us hearts of flesh, and sending His Spirit to lead us in obedience to the Torah (Ezekiel 36:26-27), and God putting the Torah in our minds and writing it on our hearts (Jeremiah 31:33).
There was nothing about the veil being torn that means that the Torah is obsolete. Likewise, there was nothing about the destruction of the 1st Temple that caused the Torah to become obsolete, so there is also nothing about the destruction of the 2nd Temple that caused it to become obsolete. In Titus 2:14, Jesus gave himself to redeem us from all lawlessness and to purify for himself a people of his own possession who are zealous for doing good works, so the way to believe in what he finished through the cross is by repenting and becoming zealous for doing good works in obedience to the Torah.