All men have been called to be "obedient to the faith".
Obedience in the New Covenant of the gospel of the grace of God is relying on Jesus for righteousness and goodness and life and blessing and salvation in all it's different aspects.
Disobedience to the faith in the New Covenant is relying on our own righteousness, our own doing of good.
Romans 10:2-3 (NASB)
[SUP]2 [/SUP] For I testify about them that they have a zeal for God, but not in accordance with knowledge.
[SUP]3 [/SUP] For not knowing about God's righteousness and seeking to establish their own, they did not subject themselves to the righteousness of God.
Philippians 3:9 (NASB)
[SUP]9 [/SUP]and may be found in Him, not having a righteousness of my own derived from the Law, but that which is through faith in Christ, the righteousness which comes from God on the basis of faith,
The law is what people did or didn't do for their own righteousness.
All works-based righteousness is based on this truth and it is NOT the gospel of the grace of God in Christ. It is a religion.
Being "obedient to the faith" is believing in Christ and His work for us for life and living.
Notice here in Acts 6:7 that even the "good moral living" - law-keeping priests need to be "obedient to the faith".
The keeping of the law of Moses is NOT the same as being "obedient to the faith".
Acts 6:7 (NASB)
[SUP]7 [/SUP] The word of God kept on spreading; and the number of the disciples continued to increase greatly in Jerusalem, and a great many of the priests were becoming obedient to the faith.
Pagans/Gentiles also need to be "obedient to the faith" and believe in Christ and what He has done for life and living.
Romans 1:5 (NASB)
[SUP]5 [/SUP] through whom we have received grace and apostleship to bring about the obedience of faith among all the Gentiles for His name's sake,
All people of all types are called to be "obedient to the faith" - which is belief in Christ alone for life and living.
Romans 16:26 (NASB)
[SUP]26 [/SUP] but now is manifested, and by the Scriptures of the prophets, according to the commandment of the eternal God, has been made known to all the nations, leading to obedience of faith;