puritanical

Strict, straight laced, and unsmiling, someone who is puritanical follows moral or religious rules to the letter.

Describing someone as puritanical is usually a bit of a criticism, since the word implies that the person is not just religious, but overly rigid in his or her beliefs and not a lot of fun to be around. It stems from the word "Puritan," a believer in the branch of Protestantism that objected to some practices of the Church of England. Its root, in turn, is thought to be purity, which is what puritanical people seek when they stick to the rules.