They would definitely seem inextricably contradictory like all those other instances wherever we find the necessity of works or righteousness to inherit life, when you have a dogma of faith-alone, not works or anti-works. If you could only forget your preconceived dogmas for a moment to interpret the passage, and read it with a fresh mind, it might help you.
Paul commands the Philippian church, as do the other apostles in their epistles, to obey God and work out their own salvation with fear of God.
Work out your own salvation
- Holman Bible Dictionary on Fear:
The “God-fearers” The “God-fearers” were those who were faithful to
God and obeyed His commandments (Job 1:1; Psalm 25:14; Psalm 33:18 ).
Those who fear God are blessed (Psalm 112:1 ); they enjoy God's
goodness (Psalm 34:9 ) and God's provision (Psalm 111:5 ). In the New
Testament “God-fearers” became a technical term for uncircumcised
Gentiles who worshiped in the Jewish synagogue.
Fear in the New Testament Some Christians tend to de-emphasize the
fear of God in the New Testament by placing the love of God above the
fear of God. There is indeed a greater emphasis on the love of God in
the New Testament. However, the element of fear was part of the
proclamation of the early church.
Paul admonished believers to work out their salvation “with fear and
trembling” (Philippians 2:12). The early church grew in number as
they lived “in the fear of the Lord” (Acts 9:31 ). The fear of God is
related to the love of God. The revelation of God to people in the New
Testament contains the element of God's mysterious otherness calling
for reverent obedience. The New Testament church stands in awe and
fear in the presence of a holy God, for fear is “the whole duty of man” (Ecclesiastes 12:13).
Whoever is doing righteous works with Godly fear, is doing the works of God. In the Hebrew way of saying, God is working in them, or through them (v2.13); after all, the purpose of the elect is to be the workmanship, created in Christ Jesus for good works, which God afore prepared that we should walk in them Eph 2:12. And that God shows no partiality, but in every nation anyone who fears him and does what is right is acceptable to him Acts 10:34-35. He who does the works of God is a child of God; and he who commits sin is of the devil. God is working in the righteous, and Satan is working in the unrighteous.
[1John 3:7-10 RV] My little children, let no man lead you astray: he that doeth righteousness is righteous, even as he is righteous: he that doeth sin is of the devil; for the devil sinneth from the beginning. To this end was the Son of God manifested, that he might destroy the works of the devil. Whosoever is begotten of God doeth no sin, because his seed abideth in him: and he cannot sin, because he is begotten of God. In this the children of God are manifest, and the children of the devil: whosoever doeth not righteousness is not of God, neither he that loveth not his brother.
Righteousness of my own, which is against the righteousness of God
[Rom 10:3-6 NHEB] For being ignorant of God's righteousness, and seeking to establish their own righteousness, they did not subject themselves to the righteousness of God. For Christ is the end of the law for righteousness to everyone who believes. For Moses writes about the righteousness of the law, "The one who does them will live by them." But the righteousness which is of faith says this, "Do not say in your heart, 'Who will ascend into heaven?' (that is, to bring Christ down);
The righteousness of my own in Phil 3:9 refers to obsolete law based righteousness, which is no longer valid, and hence, is not the righteousness criterion of God. The law is no longer (Gal 3:18, 25) the acceptable way of righteousness because it has been finished by Christ who gave a new superior covenant. Faith in Christ has replaced the whole law of Moses. Christ is the end of the law based righteousness, or Christ has ended the law. Now, after Christ, the acceptable way of righteousness according to God, is based on faith in Christ. If I refuse God's new covenant and still cling onto the old one, which has been nullified, then I am establishing my own righteousness which is against God's.
I don't find any contradiction, except the contradiction arising from your hermeneutics as you write:
Salvation is to be justified by faith not of any good works referencing the epistles Romans 1:17, Galatians 2:16, and Ephesians 2:8-9. ("His faith is credited as righteousness" Romans 4:5)
Nowhere does any passage indicate that justification by faith is contrasted with "good works". Eph 2:8-9 and Titus 3:5 only refers to the gracious sacrificial atonement of Christ, which is not given due to good works of any men, but freely out of the mercy of God. That is unrelated to the fact that the forgiveness from that atonement, still requires good works from men, see Matthew 25 to be saved. Galatians 2:16 states yet we know that a person is not justified by works of the law but through faith in Jesus Christ, so we also have believed in Christ Jesus, in order to be justified by faith in Christ and not by works of the law, because by works of the law no one will be justified. The new way of righteousness, faith in Christ is contrasted with "works of the law" or the law, not with "good works". If you confuse between the law works with general moral works or any works of righteousness and obedience, then you will always have inextricable contradictions between your dogma and the whole Bible. The kinds of the hundreds of different questions we keep seeing on this topic. The error is in your fallacious association of works of the law, with good works, when Paul was unambiguous in all his epistles that he only debated against the dead works of the law, because the law covenant is no longer valid.