Father Peregrine is a playful priest. (And evidently an alliterative one, too.) He might start off looking like a silly joker, but we quickly learn that he's deeply religious. He searches his heart to make sure his motivations are pure. So we're kind of on his side because he seems aware of his own potential flaws. For instance, he goes to convert the Martians to Christianity, which seems adventurous, but he wants to make sure he's doing it for the greater glory of God, not just to make himself look good.
And no matter how you personally feel about this kind of missionary work, Father Peregrine just sounds like a nice guy. Listen to the way he talks about the Martians:
We'd like to know about the Martians. For only if we know about them can we plan our church intelligently. Are they ten feet tall? We will build large doors. Are their skins blue or red or green? We must know when we put human figures in the stained glass so we may use the right skin color. Are they heavy? We will build sturdy seats for them. (39)
If you have to convert people, this is the way to do it. Instead of forcing the Martians into some preconceived mold, Father Peregrine is ready to adapt and change. Like Bradbury's other protagonists, he has an open, curious mind, and he's ready to appreciate Mars for what it is.
So if Father Peregrine is open and curious, it's a pretty good bet that Father Stone is going to be rigid and inflexible. You know, like a stone.
And guess what? He is. He's hard and dogmatic, with no sense of humor. And that's about all we know about him. He's pretty much there to serve as a foil to Peregrine.