I am also in the US and use my home-rendered tallow to make soap. Disclaimer: I don't really sell per se, but donate soap and cosmetic products to organizations that do sell, and also make custom orders for friends.
My understanding is that, absent specific state or local regulations, small sellers of true soap (as defined by MOCRA) are exempt from the requirements as long as they make no claims and use no ingredients that put it into the cosmetic or drug categories. But if you are making and selling things that fall into the cosmetic category, then you are subject to keeping batch records, using compliant labeling, etc.
Here is a link to read more about that.
Of course, most soap sellers do label their soap with ingredients, out of deference to those who might have allergies. If you want to learn more about labeling,
Marie Gale is the best source and authority for that.