"God...protect us from the innocent and the good," says Fowler. What did he mean, and how does it relate to the novel's message?
I believe this refers to the British Fowler's cynicism over the "do-gooder" Americans and their social agendas in Vietnam, which in turn relates to Greene's theme: whether or not one country should become involved in the wars (or affairs) of other.
As to the meaning of your quote, here is an additional quote that I think shows Fowler's position on meddling more clearly. (He's against it!) Fowler says:
"Innocence is like a dumb leper who has lost his bell, wandering the world, meaning no harm. You can't blame the innocent, they are always guiltless. All you can do is control them or eliminate them."
This quote can also be applied to the second theme of the book dealing with human motivation. It is ironic because Fowler keeps repeating that he is not involved, perhaps to convince himself. But he eventually gets personally involved, to the point that he's an accomplice to murder. What is suspicious is why Fowler gets involved. What are his motives? Is it because of his compassion for the Vietnamese people, or is it because of his desire for Phoung? The ending doesn't make the answer clear. Fowler says himself that "I had become as engaged as Pyle, and it seemed no decision would ever be simple again."