Tired of always playing the same roles, Little Red Riding Hood, her grandmother and the Wolf demand a new version of the tale. The story then plays out in a more contemperary urban environment, with Little Red Riding Hood working as a pin-up girl in a night club.
Technically harm does come to an animal throughout the film, but the animal in question is an overtly-anthropomorphic wolf who deserves all the cartoony violence he suffers.
A male wolf sexually harasses a female nightclub singer. Later, the tables are turned and the wolf gets chased around by the young woman's grandmother. This is played for comedy.
The attempted sexual assault of a male wolf by an older woman is played for comedy and framed as comeuppance for his previous harassment of a young woman.
The wolf ends the film by shooting himself in the head after saying he'll kill himself "if he ever even looks at another dame". Immediately after, the titular Red reappears for her next performance and the wolf makes good on his word.