Interesting, but it's not very common at all; at least in the West. I don't even know if stuff with baby parts is legal or approved on the market here. Asians do use weird stuff like snail mucin, antler velvet and placenta (IDK if human but you see a lot of animal placenta in their products made for skincare).They also use foreskins from circumcised babies.
The biggest skincare ingredients such as AHAs, BHAs, PHAs, antioxidants, hyaluronic acid, polyglutamic acid, colloidal oatmeal, peptides, retinol etc. have nothing to do with baby parts though afaik. A lot of them can be synthesized from plants or processed minimally like with oatmeal.
I'm guessing this stuff never took off with the plant based craze and all since the 2010s at least. People lose their shit even at lanolin nowadays.
This conversation reminds me of when Mr. Amhole (Kevin Gibes) bragged about getting corpse skin (alloderm) in his neovag. This inspired a bunch of people in the thread to apparently get off the organ donor list, lol.