What connects “dripping with gore” and Buddhism & Christianity in “The Dagger with Wings”?

Question

In "The Dagger with Wings" by G. K. Chesterton, Father Brown was explaining some philosophical aspects of the murderer, saying:

It was his whole game with me to be as idealistic as possible; and whenever that is attempted by that sort of man, you will generally find it is that sort of ideal. That sort of man may be dripping with gore; but he will always be able to tell you quite sincerely that Buddhism is better than Christianity. Nay, he will tell you quite sincerely that Buddhism is more Christian than Christianity. That alone is enough to throw a hideous and ghastly ray of light on his notion of Christianity.”

What's the relationship between "dripping with gore" and Buddhism & Christianity?

And in a later paragraph, he say:

It isn’t defending a man to say he is a genius,” said Father Brown. “Far from it. And it is simply a psychological fact that an artist will betray himself by some sort of sincerity. Leonardo da Vinci cannot draw as if he couldn’t draw. Even if he tried, it will always be a strong parody of a weak thing. This man would have made something much too fearful and wonderful out of the Wesleyan Methodist

What's exactly meant by an artist will betray himself by some sort of sincerity?

Answer 1

"Dripping with gore" indicates that the man had just committed a violent murder and was literally dripping with blood from the victim. However if he were philosophically inclined, he could hold forth on views that Buddhism was better than Christianity -- or, in view of the way Father Brown is discussing European criminals, those notions of Buddhism that were current in the knowledge of the time. The reincarnation and re-occurrence that Father Brown mentioned were common knowledge and derived, however distantly, from Buddhism.

The betrayal bit means that when trying to pretend to be something he's not, he will accidentally say what he sincerely believes. This will give away the pretense.