The faith of Christ
Whether 'faith of Christ' names faith in Christ or Christ's own faithfulness.
Galatians 2:15-21
15“We, being Jews by nature, and not Gentile sinners,
16yet knowing that a man is not justified by the works of the law but through faith in Jesus Christ, even we believed in Christ Jesus, that we might be justified by faith in Christ, and not by the works of the law, because no flesh will be justified by the works of the law.
17But if while we sought to be justified in Christ, we ourselves also were found sinners, is Christ a servant of sin? Certainly not!
18For if I build up again those things which I destroyed, I prove myself a law-breaker.
19For I, through the law, died to the law, that I might live to God.
20I have been crucified with Christ, and it is no longer I who live, but Christ lives in me. That life which I now live in the flesh, I live by faith in the Son of God, who loved me, and gave himself up for me.
21I don’t reject the grace of God. For if righteousness is through the law, then Christ died for nothing!”
What each tradition says
Rabbinic / Midrashic
Kohler argues that Paul locates the saving grace of God in faith (blind belief), not in the works of the Law. Paul declares faith in Jesus' atoning death, not the Law, to be the means of justification and salvation; the Law demands servitude, while the Spirit of Christ makes people children of God.
Kaufmann Kohler, Paul of Tarsus (Jewish Encyclopedia, 1901-1906) — Section 'Antinomianism and Jew-Hatred' (Paul's doctrine of faith)
Patristic
Chrysostom states that we have relinquished our habitual mode of life and taken ourselves to the faith which is in Christ. This describes a movement from one's former manner of life to the faith that is in Christ.
John Chrysostom, Homilies on the Epistle to the Galatians (NPNF1-13, ed. Schaff) — Homily on Galatians ii (on Gal. ii. 15-16)
Catholic
Haydock says false doctors teach we are not justified except by the ceremonies and works of Moses' law, though we seek justification in Christ by faith in him and by his grace. If so, this blasphemous consequence must follow: Christ is minister and author of sin, making us believe faith in him and compliance with his doctrine justify and save.
George Leo Haydock (Witham notes), George Haydock's Catholic Bible Commentary (1859), on Galatians 2:16 — Comment on Galatians 2:16 (justified 'in Christ, by faith in him')
Orthodox
No sourced position found. Checked Philaret's Longer Catechism (pravoslavieto.com): its justification materials do not gloss the genitive 'faith of Christ'; The Acts and Decrees of the Synod of Jerusalem (Robertson 1899, archive.org actsdecreesofsyn00orth): refutes the Calvinist chapters/answers but never treats Gal. 2:16; CCEL NPNF1-13 (Chrysostom on Galatians) is patristic, not a distinct Orthodox voice; no public-domain English Orthodox commentary on Galatians found (Theophylact's English is modern/copyrighted).
Reformed / Protestant
John Gill says the phrase "faith of Jesus Christ" does not mean the faith Christ himself had as a man in God, by which he trusted God's promised help. Instead, it means the faith that has Christ as its object, author, and finisher.
John Gill, John Gill's Exposition of the Whole Bible, on Galatians 2:16 — Exposition of Galatians 2:16 (rejects the 'faith Christ had' reading)
Evangelical
John Wesley’s note on Galatians 2:16 states that “the faith of Jesus Christ” means faith in him. The phrase is understood as faith in Jesus Christ.
John Wesley, John Wesley's Explanatory Notes on the Bible, on Galatians 2:16 — Note on Galatians 2:16