Why do they use red filters in dark rooms?

Photographic film is not light sensitive to red light ...

2nd Answer:

Actually, that is not true. When you are working with photographic film, any light at ALL will 'fog' the film and ruin your photos.

Photo paper is nowhere near as sensitive to red light as film is, so you can use a red "safe" light so you can see what you're doing as you print, develop, stop, and fix your photo prints. The room lights may be on as you rinse the print.