Which "saved" are you asking about: delivery from bondage to sin or transformation of mortal bodies to immortal?
Does anyone - Jew or gentile - need to offer up animal sacrifices today? No. Because that's specifically what the Messiah came to perform. This is why the study of the OT is important so that we can understand which "law" Paul is referring to when he mentions "law" from Romans to Galatians.
Every law is broken into two categories (this is true within any society, including the Kingdom of God):
1) Laws to abide by as a just person (to avoid committing a crime)
2) The steps to perform to pay for a crime (once committed), to restore one's right standing in the law
The law of Almighty is broken into two categories:
1) The Commandments to obey as a just person (to avoid sin)
2) The works of the law to perform to cleanse sin (once committed), to restore one's right standing in the law
The law of Almighty before the cross:
1) The Commandments to obey as a just person (to avoid sin)
2) Blood rituals (i.e. animal sacrifice) and cleansing rites >>> did nothing but point to Messiah's work
The law of Almighty after the cross (law changed, not ended; Hebrews 7:12):
1) The Commandments to obey as a just person (to avoid sin) >>> gifts given to perform (Holy Spirit, Grace, ministries, etc)
2) Messiah performs cleansing rituals in heaven w/His blood >>> requires our faith (because we can't see it from down here)
It's the book of Hebrews that says the law was changed by necessity because of a change of priesthood; a critical bit of information that we miss when we ignore this book.
What's more, the following shows the audience or groups Paul visited during his ministry (Peter's letter was added to show who was in Galatia):
Rome - Jews & Gentiles
Romans 1:7
7 To all that be in Rome, beloved of God, called to be saints: Grace to you and peace from God our Father, and the Lord Jesus Christ.
Acts 28:16-17
16 When we arrived in Rome, Paul was permitted to stay by himself, with a soldier to guard him.
17 After three days, he called together the leaders of the Jews. When they had gathered, he said to them, “Brothers, although I have done nothing against our people or the customs of our fathers, I was taken prisoner in Jerusalem and handed over to the Romans.
Corinth - Jews & Gentiles
1 Corinthians 1:2
2 Unto the church of God which is at Corinth, to them that are sanctified in Christ Jesus, called to be saints, with all that in every place call upon the name of Jesus Christ our Lord, both theirs and ours:
Acts 18:1,4
1 After this, Paul left Athens and went to Corinth...4 And he reasoned in the synagogue every sabbath, and persuaded the Jews and the Greeks.
Galatia - Jews & Gentiles
Galatians 1:2
2And all the brethren which are with me, unto the churches of Galatia:
1 Peter 1:1
Peter, an apostle of Jesus Christ, To God's elect, exiles scattered throughout the provinces of Pontus, Galatia, Cappadocia, Asia and Bithynia,
Ephesus - Jews
Ephesians 1:1
1 Paul, an apostle of Jesus Christ by the will of God, to the saints which are at Ephesus, and to the faithful in Christ Jesus:
Acts 18:19-21
19 And he came to Ephesus, and left them there: but he himself entered into the synagogue, and reasoned with the jews. 20 When they desired him to tarry longer time with them, he consented not; 21 But bade them farewell, saying, I must by all means keep this feast that cometh in Jerusalem: but I will return again unto you, if God will. And he sailed from Ephesus.
Philippi - Jews & Gentiles
Philippians 1:1
1Paul and Timotheus, the servants of Jesus Christ, to all the saints in Christ Jesus which are at Philippi, with the bishops and deacons:
Acts 16:11-13
11 Therefore loosing from Troas, we came with a straight course to Samothracia, and the next day to Neapolis; 12 And from thence to Philippi, which is the chief city of that part of Macedonia, and a colony: and we were in that city abiding certain days. 13 And on the sabbath we went out of the city by a river side, where prayer was wont to be made; and we sat down, and spake unto the women which resorted thither.
Colosse/Phrygia - Jews & Gentiles
Colossians 1:2
2 To the saints and faithful brethren in Christ which are at Colosse: Grace be unto you, and peace, from God our Father and the Lord Jesus Christ.
Acts 2:10; 16:23
10 Phrygia, and Pamphylia, in Egypt, and in the parts of Libya about Cyrene, and strangers of Rome, Jews and proselytes,
23 And after he had spent some time there, he departed, and went over all the country of Galatia and Phrygia in order, strengthening all the disciples.
Thessalonica - Jews & Gentiles
1 Thessalonians 1: 1
1 Paul, and Silvanus, and Timotheus, unto the church of the Thessalonians which is in God the Father and in the Lord Jesus Christ: Grace be unto you, and peace, from God our Father, and the Lord Jesus Christ.
Acts 17:1-4
1 Now when they had passed through Amphipolis and Apollonia, they came to Thessalonica, where was a synagogue of the Jews: 2And Paul, as his manner was, went in unto them, and three sabbath days reasoned with them out of the scriptures, Opening and alleging, that Christ must needs have suffered, and risen again from the dead; and that this Jesus, whom I preach unto you, is Christ. And some of them believed, and consorted with Paul and Silas; and of the devout Greeks a great multitude, and of the chief women not a few.
Timothy - A mixed Jew-Greek
1 Timothy 1:2
2 Unto Timothy, my own son in the faith: Grace, mercy, and peace, from God our Father and Jesus Christ our Lord.
Acts 16:1
1 Then came he to Derbe and Lystra: and, behold, a certain disciple was there, named Timotheus, the son of a certain woman, which was a Jewess, and believed; but his father was a Greek:
Titus - A Gentile Proselyte "strongly tied" to the synagogue in Corinth
Titus 1:4
4 To Titus, mine own son after the common faith: Grace, mercy, and peace, from God the Father and the Lord Jesus Christ our Saviour.
Acts 18:7 [Grk original]
And he departed thence, and entered into a certain man's house, named [Titus] Justus, one that worshipped God, whose house joined hard to the synagogue.
Philemon - A believer from Colosse (a Jew & Gentile community; see above)
Philemon 1:1-2
Paul, a prisoner of Jesus Christ, and Timothy our brother, unto Philemon our dearly beloved, and fellowlabourer, 2 And to our beloved Apphia, and Archippus our fellowsoldier, and to the church in thy house:
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Paul's audience was a mixture of Jew and gentile proselytes.