I wouldn't
be to concerned about the animal fat!
As long as there is a demand for meat by meat eaters, there is going to be animals butchered to meet that demand.
At that point in time, there isn't a reason to simply throw away the fat that nobody's going to eat. That would be wasteful.
There are many types of fats, be they animal, or vegetable. What's interesting is that each fat is unique, in that each fat has its own fatty acid makeup. These specific fatty acids are used for thousands of things from medicine, food additives and of course soap!
From a science and chemistry perspective there isn't a concern about where that fatty acid came from, because the same fatty acid
(say oleic acid for instance) can be found in vegetable oil (olive) and lard! (pig fat)
Two completely different fats that contain a similar fatty acid makeup.
Since a cleaning formula, or detergent may require the addition of a percentage of actual soap to perform efficiently, why would they use... say palm oil (that's not always sustainable) rather than using tallow that has a very close fatty acid makeup, and would be thrown away otherwise.