Generally speaking, most skincare products are safe to use while breastfeeding, but there are a few ingredients that dermatologists recommend avoiding.
Here's a short list:
Retinol
Hydroquinone
Salicylic acid
Why?
The recommendation to avoid these products while breastfeeding is due to an abundance of caution drawn from research published by the Infant Risk Center in which those three ingredients were shown to cause congenital disabilities during pregnancy.