Like mince pies in the UK, mooncakes were originally meat-based but slowly changed into mainly sweet confections, although often with surprisingly salty centres of preserved egg to represent the moon. A few meat based examples still exist in China, but are rare.
That said, I've never come across the ones in @rarerollingobject's post, even in Suzhou.
As to the red stamp, that is universal in China. A legal document isn't legal without a red stamp. All examples of Chinese art and calligraphy etc are completed with the artists red seal. Exam paper results are given by red stamps. Dim sum foods often have red marks to indicate the contents of buns etc. When I go to the supermarket, the till receipt has to have a red stamp. I never stand still too long in case someone stamps me!
When I first came to China, I was required to have a full medical examination. I did this in one of the world's top international hospitals (in Harley St, London). When I got to China it was rejected because there was no red stamp. If I had known, I could have stamped anything on it so long as it was red. I was made to redo the examination in the most backward, dirty, incompetent hospital on the planet. But they had a red stamp so that was OK.
