There are multiple places the color of the movie you watch are determined: There is the characteristic curve of the film used to capture the image and make the print, then there is the way the film fades over the course of time, then there is the way the film is transferred to digital media or magnetic tape. If the movie you're watching was recorded for TV broadcast in the United States, for example, it was encoded in NTSC colors, which have a very limited color pallette. If the film hasn't been re-digitized from the original film for HDTV, the color will be terrible. Finally, a colorist could re-interpret the colors of old film for a modern release. The color space of projected film is larger than that of even a good HD screen, there is no bright line between an "accurate" adaptation and "creative enhancement".

I'm actually a photo tech at a cultural institution, but I work with mostly B+W film, I'm not terribly familiar with historical color materials, and have only worked with still photographic film.

It was because Hollywood used film stock that would lose color over a period of time. Blue would go first and eventually all that would be left was red. This also happened with slide film with the notable exception of Kodachrome. Around 1980 a serious effort was made to solve this problem:

Fabulous Technicolor! A History of Low Fade Color Print Stocks