This is not correct. Soap dissolves proteins quite well. It is even the basis for many standard protein biochemistry techniques which I use every day. Small, delicate tissues will completely dissolve in 10 minutes if heated in a 1% detergent solution. (It is true that proteins in connective tissue (e.g. collagen, keratin) will not be dissolved by soap alone because they are covalently cross-linked.)
Perhaps you are making a distinction between a protein or fat being “in solution” vs in a detergent micelle or emulsion? If so, it’s not a very important distinction for the OP’s question.
For examples on what perfused mild detergents do to an organ, see here. Those particular protocols have been optimized to keep the extracellular matrix intact. Longer, harsher treatments, combined with a bit of mechanical disruption, would make those decellularized organs unrecognizable.