Nowadays, it seems people think of "faith" as religious faith, but if it only referred to religion, people wouldn't say "faith in God." For there to be a modifying phrase like that shows that there are other kinds of faith (and the phrase "religious faith" also is qualified with a descriptive word).
"To keep faith" means to maintain a relationship of trust and trustworthiness with another person. "To keep faith with one's lord" was to be faithful, and worthy of his faith in you. So faith would be made up of loyalty, reliabiity and truthfulness. Keeping one's oaths and obligations is keeping faith.
—Ælflæd of Duckford