Paul ends the previous section with the command: "rejoice in the Lord" (3:1a). And with this, he calls us to be a community of joyful saints, rid of the interpersonal conflicts so common in the world. Paul then in 3:1b moves on to a new topic to guard us against the foolish practice of trusting in the flesh.
Trust in the Flesh (2): Paul gives a scathing description of unconverted Jews who put their confidence in their lineage and religious accomplishments, thinking these are valuable. But how foolish! These, in and of themselves, amount to nothing in the eyes of God. So, Paul shows their foolishness and calls them for who they really are before God: "dogs" (ceremonially unclean), evil-doers ("evil workers") and "false circumcision" (outside the covenant).
Boast in Christ (3): Contrasted from these are believers in Christ whom he calls "the true circumcision." Even though the Philippians are Gentiles, God regards them as His covenant people ("true circumcision") because they have the true mark of being His people: the circumcision of the heart. And as a result, they worship God "in the Spirit of God," which is nothing like how the Jews historically feigned "worship." Paul also adds here that believers "glory in Christ Jesus." Their boast is in the Messiah because it is in Him that they have a righteous standing before God and eternal glory—something truly valuable. They trust in Christ and "put no confidence in the flesh." A proper faith-relationship with Jesus Christ is the only way to God's blessing.
Example (4-6): Paul then shows from his own life how foolish it is to trust in the flesh. He once thought that his impressive Jewish pedigree and religious achievements were a great gain to him. But they all turned out to be completely worthless in giving him anything of value in the presence of God. None of these added to his righteous standing before God: being ceremonially circumcised ("on the eighth day"), or coming from the chosen nation ("of the nation of Israel"), or having a traceable ancestry ("a Benjaminite"), or having pure Jewish blood ("a Hebrew from Hebrews"), or being a respected law-keeper ("a Pharisee"), or zealously warring the infidels, or being blameless in Pharisaic legalism. The only way to obtain the blessing of God (and the righteousness from God) is trusting His Messiah. One who yearns for the acceptance and the recognition of God puts his wholehearted confidence in Christ. No earthly merits will ever give him the desires of his heart.
 NASB starts 3:1 with "Finally." This is the Greek phrase to loi-pon (τὸ λοιπόν) and it can also mean "so then" or "so that" (as in 1 Cor. 7:29). "So then" fits best here and this marks a bookend to the commands to rejoice given earlier (2:17-18). Paul will once more repeat this imperative in 4:4, "Rejoice in the Lord."
 "trust" is just another translation of "put confidence in" which is the Greek verb pei-thō (πείθω) in 3:3-4.
 Paul explains "trust in the flesh" in 3:4-6 as dependence on ancestry and religiosity as merits before God.
 These are unconverted since Paul distinguishes them from "we [who] are the true circumcision…" (3:3).
 Contra true believers, these Jews do "put confidence in the flesh."
 Similar language "deceitful workers" in 2 Cor. 11:13 meant "deceivers." So it should be here: "evil-doers."
 Their circumcision was "mutilation," or ka-ta-to-mē (κατατομή), only a surgery, with zero spiritual value.
 They were physically uncircumcised. First converts in Philippi were Lydia, a proselyte (Acts 16:14, "worshipper of God [common expression for proselytes]") and a Roman Jailer's household (Acts 16:29-34).
 "circumcision… of the heart" (Rom. 2:29) is the true sign. Cf. also Deut. 30:6; Jer. 4:4 and Acts 7:51.
 The Jews offered God "worthless offerings… an abomination to Me… a burden to Me" (Isaiah 1:11-14).
 "glory" is kau-cha-o-mai (καυχάομαι) which also means "boast." The cognate "reason to glory" was in 2:16.
 Cf. 3:9 ("the righteousness which comes from God") and 3:20-21 ("conformity with the body of His glory").
 Given Paul's example of the flesh in 3:4-6, "flesh" here points to human achievement and heritage.
 This phrase is more literally "out from [ek (ἐκ)] the nation of Israel." Paul points to national origins.
 He not only can trace his genealogy to this tribe, but he was even named after the first King of Israel, "Saul."
 He was a Hebrew who comes "out of [ek (ἐκ)] Hebrews." The plural points out both parents were Jewish.
 Paul believed he was being zealous for God in persecuting the Way "to the death" (Acts 22:3-4).
 "the righteousness which is in the Law [lower case "law" in ESV, NET, NKJV]" is Pharisaic righteousness per tradition of the elders (Mark 7:1-8), not Mosaic Law. Paul just asserted in 3:5: "as to the Law, a Pharisee."