No. This is one of the few places where the right answer goes directly against what most people would expect.
When caring for an open surgical wound, do not use skin cleansers, alcohol, peroxide, iodine, or soap with antibacterial chemicals. These can damage the wound tissue and slow healing.
Soap with antibacterial chemicals sits in that list alongside alcohol and peroxide, and the reason is the same for all of them. The problem is not that they fail to kill bacteria. It is what they do to the tissue that is trying to heal.
That makes the difference a narrow one on a store shelf, so it’s worth being precise. Mild soapy water, gentle soap and water, and warm water and soap are all recommended across four different wound types. Soap is not the problem. The word on the label is.
Soap also has a place in wound care that isn’t inside the wound, and the two get confused. Handwashing before a dressing change matters a lot. Wash your hands using soap, for 15 to 30 seconds, cleaning under your nails, or use an alcohol-based cleanser. Antibacterial agents on your hands before the dressing change are a different question from antibacterial agents in the wound.
If an antibacterial soap has been used on a wound, this is not a crisis. But it is worth stopping, and worth mentioning if the wound has become more painful or has stopped making progress.