This is a two-fold question which I will answer in the reverse order:
1. Scripture to support termination of Levitical/ceremonial laws
Probably the earliest is the conclusion of the first council of Jerusalem as recorded in Acts 15 as a result of this very debate - should gentiles who become Christians keep the ceremonial law as typified by the rite of circumcision - ANSWER - NO but they still needed to keep the moral and Noahide laws, Acts 15:28, 29 -
It seemed good to the Holy Spirit and to us not to burden you with
anything beyond these essential requirements:
- You must abstain from food sacrificed to idols (Moral requirement in the 10 commandments)
- from blood (Noahide law from Gen 9:4)
- from the meat of strangled animals (Noahide law from Gen 9:4)
- and from sexual immorality (moral law from 10 commandments)
You will do well to avoid these things.
Thus, the Levitical/ceremonial laws were officially terminated; however, the Levitical covenant (Lev 1-9, 16, 21-27 , Num 3, 4, 8, 18, 25:10-13, Deut 33:8-11, Neh 13:29, Mal 2:4-8) which was an eternal covenant (Num 25:12, 13, Ps 106:30) is fulfilled in Christ as our Great High Priest (Heb 4:14-16, 5:10, 7:23-28, 8:1, 2, 9:1-28, 10:1-18) and our Passover Lamb (, John 1:29, 1 Cor 5:7, 1 Peter 1:19), etc.
This is confirmed when Jesus died on the cross, the ceremonial system was finished and the temple curtain dividing the Holy from the Most Holy Place was torn in two from top to bottom (Matt 27:51, Mark 15:38, Luke 23:45, see also 2 Cor 3:13-16) to symbolise this. Jesus became the High Priest of the New Covenant (Heb 4:14-16) and fulfilled the Levitical Covenant.
2. When did The Christian Church abandon the Ceremonial/Levitial laws?
Despite the clear decision of the First Jerusalem council as documented above, that did not silence agitation and descent. The final blow came with the destruction of the Jerusalem temple and its associated priesthood in 70 AD. After that, keeping of the Levitial and ceremonial law became impossible, even for those who wanted to keep it.
APPENDIX - Different laws
I agree with the OP that there is little in the Torah that distinguishes civil vs ceremonial vs moral laws from each other. To try to do so is to ask the wrong question. Law in the OT context had no meaning outside an accompanying covenant - the law was to regulate the relationship between the two parties making a covenant. There are several such covenants in the OT, each with an associated law:
- Noahide Covenant: Gen 8:20 – 9:17
- Abrahamic Covenant: Gen 15, 17, 18:9-15, 22:15-18
- Israelite Covenant: Exodus 19-24, and expanded in parts of Leviticus, Numbers and Deuteronomy – often called, “The Old Covenant”, or, “Moral Covenant”, or, sometimes incorrectly called, “The Mosaic Covenant”.
- Levitical Covenant: – Lev 1-9, 16, 21-27 , Num 3, 4, 8, 18, 25:10-13, Deut 33:8-11, Neh 13:29, Mal 2:4-8.
- Davidic (or Regal, or Royal) Covenant: 2 Sam 7, 23:5, 1 Kings 6:11, 12, 8:25, 1 Chron 17:11-14, 2 Chron 6:14-16, 7:17, 18, 13:5, Ps 89:4, 29, 34, 39, 132:11, 12, Jer 33:21, Eze 37:15-28.
Thus, we can now see what happened to each of these in the NT -
- The Noahide covenant was eternal, never revoked, and made with all mankind
- The Abrahamic covenant consisted of the promise of Abraham's son (and ultimately the Messiah) and the land of Canaan
- The Israelite or moral covenant was to create the people of God.
- The Levitial covenant was with the priesthood and this anticipated the great High Priesthood of Jesus - it continues today but only in Jesus.
- The Royal/Davidic Covenant was eternal and never revoked and so continues today in Jesus. Jesus is the promised King of the new Christian Community, ie, the Kingdom of Heaven, or, Kingdom of God, Luke 1:33, John 1:49, Acts 13:23, Rev 11:15. Compare Jer 33:14-17, Eze 37:22. Thus, Jesus inherits the Davidic Covenant. He is also the “Son of David” (Matt 1:1-16) and “Son of God” as predicted in the Davidic Covenant (2 Sam 7); and His kingdom will never be defeated and is eternal, Luke 1:33, Heb 1:8, Rev 11:15, compare Ps 61:7, Isa 9:7, Ps 146:10.
- The New or Christian Covenant is a direct continuation of the Old or Moral Covenant.
- The purpose of the Old Covenant is exactly the same as the New Covenant: Specifically, God said of the Christian community, “But you are a chosen people, a royal priesthood, a holy nation, a people for God’s own possession, to proclaim the virtues of Him who called you out of darkness into His marvelous light. Once you were not a people, but now you are the people of God; once you had not received mercy, but now you have received mercy.” 1 Peter 2:9, 10 (Compare Ex 19:5, 6, Hos 1:9, 4:6).
- All the promises God made under the Old Covenant to Israelites find their fulfilment in Jesus as mediator of the New Covenant to Christians, Matt 5:17, Gal 3:14, 16, 22, 29, Eph 1:18, Col 3:23, 24, 2 Cor 1:20, Rom 9:8, Heb 9:15, 11:18, 1 Peter 1:4. Thus, the New Covenant promises to save all people. For example, The Old Covenant was to save people from slavery, Ex 20:1, 2, 23:23, Deut 5:6; the New Covenant is also designed to save people from slavery (of sin), Luke 4:18, 19, John 8:32, 34-36, Gal 3:22, 5:1, 13, 14, Acts 8:23, 13:38, 39, Rom 6:14, 18, 22, 8:1-4, 20, 21, James 1:25, 1 Peter 2:16, 2 Peter 2:19, etc.
- The Jerusalem council resolution in Acts 15:28, 29 is a specific set of requirements that were repeated from the Old Covenant for the New Covenant.
- Hebrews discusses the same idea that the Moral Law of God is to be written on our hearts, Heb 8:7-13, 10:16, 17, exactly as it should have been under the Old Covenant (compare Deut 6:5, Jer 24:7, 31:33, 34, 32:38-40, 36, 26-28). Significantly, when Heb 8:10, 10:16, “I will write my law on their hearts” quotes Jer 31:33, the word used for “law” is “Torah”. This further reinforces the idea that it was the Torah and its Israelite (ie moral) Covenant that is to be kept.
- Christians were to be “called by my Name” as confirmed in Acts 11:26, just as under the Old Covenant (2 Chron 7:14, Isa 43:7, 65:1). Matt 10:22, 24:9, Mark 13:13, Luke 21:17, Acts 15:17.
- Indeed, being “called by my name” (= Christians) and imitating Christ is the seal of God and of the New Covenant as administered by the Holy Spirit, 2 Cor 1:22, Eph 1:13, 14, 4:30.