This is from Don Garlington’s PHD dissertation: The Obedience Of Faith:
“The (phrase) ‘obedience of faith’ is primarily a commitment to God’s covenant as embodied in the totality of the law of Moses; disobedience correspondingly, is predominately apostasy from the covenant. Because of this denotation of the ‘obedience of faith’ in Jewish theology, Paul’s phrase assumes the character of a manifesto that the nations can now participate in God’s new covenant apart from becoming or remaining Jewish.”