I would not say the historical context is anything significant in The Face on the Milk Carton. The book was published in 1990 and the time frame for the setting is simply supposed to be modern times.
I think some of the issues raised in the story that were (and are) particularly relevant to modern times however are probably more important when considering the context of the book. As a young adult fiction novel, this book raised several issues that were considered questionable for its targeted audience. Among these were the ideas of kidnapping, the cult community, the questioning of the "traditional" family, and the brief mention of the main character's first sexual experience (a forerunning reason for the book's addition to the banned books list).
The seriousness of its themes are what made this book the target of criticism, both positive and negative. Ironically, since 1990, television and movies have so far crossed the threshold of what was once deemed "inappropriate" that now, The Face on the Milk Carton would probably be considered mild.