A couple of the comments have mentioned the book Courtship Rite by Donald Kingsbury, and it does sound very similar to your description. But I cannot find any scene where a woman buying a baby squeezes it to check for tenderness.
The background is a vaguely Arabian Nights setting. There is a tribe called the Kaiel (named after an insect) who eat humans of low kalothi - I can't remember exactly how kalothi is defined but it's basically genetic fitness.
The Kaiel have also bred monster-women specifically for the task of producing children for meat. I'm not sure it is ever explained exactly what these are, though I'd guess they are humans bred for the purpose.
There isn't a lot said about the selling of babies at the market because it isn't a major focus of the book, and as I mentioned above I can't find any scene like the one you describe. There is a scene where the carcass of one of the monster-women is being butchered for sale:
Oelita asked to see the back room where the meat was prepared. She spoke to the
butchers gently, never showing her mind, searching theirs. They were jovial about their task as they prepared the carcass of a “machine,” the name the Kaiel
seemed to have given the genetic monster-women who bore the babies for the
“Ye covet a block o’ that thigh? Cost ye an arm and a leg, it will.” He laughed.
“Was she very old?”
“This un, ye’ll have’t’ boil. She mebe 30-40 chile down the road.”
Or another scene:
Oelita was curious to visit the meat market. No such place existed in Sorrow. There the only meat was given away at the Temple when it was freshly available, or one waited to be invited to a funeral. Here it was sold by the temples at atrocious prices. Noe bought a small jar containing two pickled baby tongues.
But that's the closest I could find.
It's also worth noting that the book was published in 1982 so it's at the edge of your time frame.