Since Baelor the Blessed thought anything Septon Barth wrote was evil, why would he then pray over dragon eggs? Wouldn’t he have thought that dragons are sinful and hellish and dangerous — totally the opposite of the peace he claimed to stand for?

I think even Baelor realized that dragons were necessary for the security of the monarchy and the strength of his family. I think what he objected to about Septon Barth was the blasphemous focus on sorcery rather than appealing to the will of the Seven.