Answer: Rambam (Maachalos Asuros 8:15) writes that while one isn’t allowed to eat non-kosher fats, one is allowed to have other forms of benefit from them.
The Beis Yosef (YD 117; 123) writes that there is a machlokes as to whether one may rub non-kosher fats into their skin. As the Mishna (Shabbos 86a) teaches us that anointing oneself on Yom Kippur is akin to drinking, the Orchos Chaim holds that one mustn’t anoint oneself with such fats. The Rashba, however, holds that one may do so. Following this, the Taz (YD 117:4) writes that one may only anoint oneself with such fats for medical reasons, etc. (See Kaf Hachaim YD 117:15). The Biur Halacha (326:10) quotes the Vilna Gaon (OC 326:10) who sides with the Taz though writes that the minhag is to allow using non-kosher soap.
Tosafos (Yoma 77a; Nidda 32a), however, disagrees, writing that this comparison only applies to oils though not to fats. As such, soap made from fats such as tallow wouldn’t be problematic. Furthermore, the comparison of anointing to drinking primarily applies to Yom Kippur and teruma.
Based on this, R’ Moshe Feinstein (Igros Moshe OC 3:62) writes that one can use medicinal creams on Pesach even though they contain chametz alcohol.
The Aruch Hashulchan (YD 117:29), Kaf Hachaim (YD 117:14; 17) and R’ Ovadia Yosef (Yechave Daas 4:43) write that since our soap is not at all edible, it poses no issue whatsoever.
In conclusion, one can use body soap even if one knows that it contains non-kosher ingredients.