Sorry to disappoint you guy's but we can go back another decade for the "pink blancmange" eating part of my childhood and Mum had a glass "rabbit-shaped" mold. So its popularity was not driven by the plastics manufacturing industry.
As for the pink colour
life in general was a lot more basic at that time* There were 97 houses in our street and these were a little bit posh we had inside toilets and a bath. Only 6 homes had a car and 3 were work ones. Only 3 houses had a phone.
Well I remember my mum did not have much choice in food colours
I did some research and this is what I found; in the early 20th century to stop people from being poisoned
The United States Food and Drugs Act prohibited the use of poisonous or harmful colors in confectionery and the coloring or staining of food to conceal damage or inferiority.
Protecting the Consumer
The federal Food, Drug, and Cosmetic Act of 1938 finally created strict rules governing the use of synthetic foods and, surprisingly, only seven colors were approved for widespread use in food and they are still on the list today. They are
Blue No. 1 (Brilliant Blue FCF), Blue No. 2 (Indigotine),
Green No. 3 (Fast Green FCF),
Red No. 3 (Erythrosine), Red No. 40 (Allura Red AC),
Yellow No. 5 (Tartrazine), and Yellow No. 6 (Sunset Yellow FCF).
So we basically had 4 colors and green was already spoken for, "the grass"
Blue rabbit? No, not really; Yellow rabbit? Urrrm!
Red rabbit OK. But blancmange is white so a few drops of red colouring and Hey presto! we got our Pink Rabbit! And since a lot of us Kids had a nice white rabbit with red eyes as a pet, well you guessed it the Pink Rabbit worked just fine.