I guess it would be more "heroic" to just keep all of his doubts to himself? I agree that he should find a new job, quit this one, and then say what he thinks. But if everyone who had doubts about certain aspects of their faith was concidered a coward, only "heros" would be left. And their numbers would be very small.
Let's be clear: "faith" can mean a religious denomination (Baptist rather than Lutheran). "Faith" should mean love and allegiance to God.
Faith is usually considered a requirement for Salvation. Faith is the antithesis of doubt. Faith is not easy. To be Faithful requires some heroism. Certainly, if a member of the Clery lacks Faith, they should resign their office.
Consider that this individual is a "leader", and doesn't believe God's word. The church is based on faith. This man lacks faith in God's word, yet pretends to believe. If the man can't confess his doubts, then he is a coward.