Prudish

[Sarah]

Like a prude; very formal, precise, or reserved; affectedlysevere in virtue; as, a prudish woman; prudish manners.A formal lecture, spoke with prudish face. Garrick.

[Sarah]

prud·ish
Pronunciation[proo-dish]
–adjective

excessively proper or modest in speech, conduct, dress, etc.
characteristic of a prude.
—Related forms
prud·ish·ly, adverb
prud·ish·ness, noun
—Synonyms 1. reserved, coy. See modest.

[Hina Muqadas]

easily shocked by rude things, especially anything relating to sex:

[Dave Paprocki]

Having or revealing a tendency to be easily shocked by matters relating to sex or nudity; excessively concerned with sexual propriety.