@Cap , Thank you for asking how we understand this passage from Galatians.
Galatians is the 'go to' passage that Christendom has long used as Paul's rebuke of the Jews and rejection of the Torah. The problem is that most Christians do not understand the context of Paul's argument or some of the language he is using, which is further exacerbated by a lack of understanding of Paul himself. So the BIG picture is necessary.
Paul was a Torah observant Pharisee, a Jew of the tribe of Benjamin. There is not a single example anywhere in Scripture of him doing something contrary to the Torah of Moses. In Acts he is recorded as only teaching on the Sabbath as the normative day of weekly worship, he keeps the feasts - even traveling to Jerusalem in haste to do so, offering sacrifices, and testifying of himself that he never broke the Law of Moses or of the Jews. Further, it is recorded that his detractors had to use false witnesses to try to establish a case against him and even then, they regarded Paul as a member of a sect of Judaism known as 'The Way.' He never converted to anything, contrary to the (uninspired) heading in your Bible at the beginning of Acts 9.
Pharisees at the time believed that to be part of God's people, one had to convert to Pharisaical Judaism as a proselyte. The code word, or abbreviated terminology was 'circumcision,' such as 'the party of the circumcision.' Proselyte conversion included not just the Biblical practice of circumcision, but taking on the full weight of the Oral Traditions, or
halacha. (pronounced halaKAH) We see Yeshua dressing the Pharisees down for this very issue on multiple occasions, the most serious being Matthew 15 and Mark 7. The 'traditions of the elders' or 'traditions of men' had largely been enacted at and after the Babylonian exile and exist
nowhere within the written Torah. Paul, having been well advanced in Pharisaic law (traditions) knew very well the whole sticky and weighty mess. (Aside: Good book to read to see the current issue debated by Jews who love Yeshua is
Rabbinic Judaism Debunked. But, before doing the 'I told you so' happy dance, there is just as much religious tradition on the Christian side that we say must be followed for salvation, too... BOTH sides are in the process of having the Father clean their houses...)
Acts 15, esp v 5 demonstrates that this false works based religious thought system was trying to infiltrate the new non-Jewish believers. Paul was livid, and rightly so. Salvation was by faith... always has been, ask Abraham! Obedience to God's Law, the Torah, has always been His expectation, but also brings life, peace, blessings, and righteousness to name a few of the Scriptural promises. Paul affirms these truths throughout his letters. The Acts 15 ruling even affirms the Torah stating that new, non-Jews will at a minimum do four things: avoid things contaminated by idols, fornication, strangled meats and blood. Then they say demonstrate an expectation that the believers will learn the Torah of Moses in the synagogue on Shabbat. (See 15:20-21)
Galatians is written within this context. Scholars debate whether it was written before or after Acts 15. I tend to think it was before with the definitive ruling of Acts 15 settling the issue that Paul was addressing.
One final challenge when we read Paul is that the Greek has only one word for law,
nomos. Paul, throughout his letters, speaks of numerous different 'laws.' While Torah is a primary subject in many places, he also speaks of the Oral Law, the law of sin, law of sin and death, law of life, etc.... In each case, we must carefully consider context to determine what he is talking about because 'law' = 'law' but 'Torah' =/= 'traditions/Oral Law.'
In Galatians, Paul is redressing his young congregation for allowing the false idea of Jewish Oral traditions from being salvific.
These are the works of the law he rails against. He is
not against the Torah. This is the difference between works salvation (oral traditions) and salvation by faith demonstrated by obedience. (Paul and James agreed, however, Paul was fighting a different battle than James in the early congregation.) And, it is
this difference that Hagar (works) and Sarah (faith) demonstrate. Abraham still had to 'perform' with Sarah to gain a son, but it was an act of faith, knowing she was barren.
I would recommend taking the time to work through the Pauline Paradox series on YouTube by 119Ministries. Part five may be the longest as it deals with the most difficult book in Scripture: Galatians.
https://www.youtube.com/results?search_query=119ministries+galatians Other shorter videos pop up with that search, though may not be as in depth and Scripture laden.
Blessings!