Puritan is a synonym of prude.

As nouns the difference between prude and puritan

is that prude is a person who is or tries to be excessively proper, especially one who is easily offended by matters of a sexual nature while puritan is (often disapproving): a puritanical person.

As an adjective puritan is

(often disapproving): acting or behaving according to the Puritan morals (e.g. propagating modesty), especially with regard to pleasure, nudity and sex.