Galatians 3:1 O foolish Galatians, who hath bewitched you, that ye should not obey the truth, before whose eyes Jesus Christ hath been evidently set forth, crucified among you?
I don't think that it makes much sense to interpret Galatians as speaking against following Christ's example of obedience to God. In Psalms 119:142, the Law of Moses is truth, Galatians criticizing them for not obeying the truth should not be interpreted as speaking against them obeying the truth. In John 17:17, it says to sanctify them in truth and that God's Word is truth, so again Galatians should not be interpreted as speaking against obeying God's Word.
2 This only would I learn of you, Received ye the Spirit by the works of the law, or by the hearing of faith?
I have notably not taken the position that the way to receive the Spirit is as the result of obeying either the Law of Moses or works of the law, but rather I agree that the way to receive the Spirit is by the hearing of faith. In Romans 3:31 and Galatians 3:10-12, Paul said that our faith upholds the Law of God in contrast with saying that "works of the law" are not of faith, so that phrase does not refer to the Law of God, but rather Paul used it to refer to the position that Gentiles are required to become circumcised in order to become saved/justified.
3 Are ye so foolish? having begun in the Spirit, are ye now made perfect by the flesh?
4 Have ye suffered so many things in vain? if it be yet in vain.
5 He therefore that ministereth to you the Spirit, and worketh miracles among you, doeth he it by the works of the law, or by the hearing of faith?
God has not spoken anything that is not in accordance with walking in the Spirit, but rather God's character traits are the fruits of the Spirit and the Law of Moses is His instructions for how to embody His character traits, which is why the Spirit has the role of leading us to obey it (Ezekiel 36:26-27) and why the Spirit has been given to those who obey God (Acts 5:32).
6 Even as Abraham believed God, and it was accounted to him for righteousness.
7 Know ye therefore that they which are of faith, the same are the children of Abraham.
8 And the scripture, foreseeing that God would justify the heathen through faith, preached before the gospel unto Abraham, saying, In thee shall all nations be blessed.
9 So then they which be of faith are blessed with faithful Abraham.
The Gospel that Jesus taught in Matthew 4:15-23 that called for obedience to the Law of Moses was in accordance with Jesus being sent in fulfillment of the promise to bless us by turning us from our wickedness (Acts 3:25-26), which is the Gospel that was made known in advance to Abraham in accordance with the promise (Galatians 3:8), which he spread to those living in Haran in accordance with the promise (Genesis 12:1-5). The promise was made to Abraham and brought about because he walked in God's way in obedience to His law, he taught his children and those of his household to do that in accordance with spreading Gospel that was made known in advance to him, and because they did that in obedience to the Law of Moses (Genesis 18:19, Genesis 26:4-5, Deuteronomy 30:16). In Psalm 119:1-3, the Law of God is how the children of Abraham know how to be blessed by walking in God's way, and in John 8:39, Jesus said that if they were children of Abraham, then they would be doers of the same works as him, so the way that the that the children of Abraham are a light and a blessing to the nations in accordance with inheriting the promise through faith is by turning the nations from their wickedness and by teaching them to do the same works as Abraham by walking in God's way in obedience to His law in accordance with spreading the Gospel. Believing this promise is the way to become righteous.
10 For as many as are of the works of the law are under the curse: for it is written, Cursed is every one that continueth not in all things which are written in the book of the law to do them.
11 But that no man is justified by the law in the sight of God, it is evident: for, The just shall live by faith.
12 And the law is not of faith: but, The man that doeth them shall live in them.
According to Deuteronomy 27-30, the way to be blessed is by relying on the Book of the Law and the way to be cursed is by not relying on it, so Galatians 3:10 should not be interpreted as Paul quoting from that passage in order to support a point that is arguing the opposite of that passage. Rather, the fact that cursed is everyone who does not continue to do everything in the Book of the Law straightforwardly means that we should continue to do everything in the Book of the Law and that those who rely on works of the law instead thereby come under that curse.
God is trustworthy, therefore His law is also trustworthy (Psalm 19:7), so the way to trust in God is by obediently trusting in His law, it would be contradictory for someone to think that we should trust in God but not in His instructions, and positions God's instructions are not of faith rather than works of the law denies the faithfulness of God. Paul associated a quote from Habakkuk 2:4 that the righteous shall live by faith with a quote from Leviticus 18:5 that the one who obeys the Law of Moses shall attain life by it, so the righteous who are living by faith are the same as those who are living in obedience to the Law of Moses. In Isaiah 51:7, the righteous are those on whose heart is the Law of Moses, and in 1 John 3:4-7, everyone who is a doer of righteous works in obedience to the Law of Moses is righteous, so the righteous living by faith does not refer to a manner of living that is not in obedience to it.
13 Christ hath redeemed us from the curse of the law, being made a curse for us: for it is written, Cursed is every one that hangeth on a tree:
God did not give His law as a curse but in order to teach us how to be blessed while lawlessness is the way to be cursed. In Titus 2:14, it doesn't say that Jesus gave himself to redeem us from the Law of Moses but in order to redeem us 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 Jesus accomplished through the cross is by becoming zealous for doing good works in obedience to the Law of Moses (Acts 21:20).
14 That the blessing of Abraham might come on the Gentiles through Jesus Christ; that we might receive the promise of the Spirit through faith.
The way that the blessing of Abraham come so the Gentiles is not by Gentiles refusing to follow the instructions that God gave for how to be blessed.
15 Brethren, I speak after the manner of men; Though it be but a man's covenant, yet if it be confirmed, no man disannulleth, or addeth thereto.
16 Now to Abraham and his seed were the promises made. He saith not, And to seeds, as of many; but as of one, And to thy seed, which is Christ.
17 And this I say, that the covenant, that was confirmed before of God in Christ, the law, which was four hundred and thirty years after, cannot disannul, that it should make the promise of none effect.
New covenants do not nullify the promises of covenants that have already been ratified, so all of God's covenants are eternal and cumulatively valid.