Tallow and lard were used for laundry due to it being abundant and easy to find, not because its superior at cleaning.
We now know and have access to better oils for laundry, coconut being the preferred.
Lard soap is very mild with low lather. Tallow is a bit more cleansing and lathery but not a lot.
I really suggest not making a 100 tallow soap, especially deer. It will be incredibly hard and brittle.
Even 80% tallow and 20% coconut would be more balanced.