Several articles present studies that conclude that the antimicrobial soap they have tested, is not more effective than regular soap. This one, for instance.
I took part in an exercise like this myself at my university, where the antibacterial soap actually removed less bacteria than any other soap tested. Even less than the normal soap of the same brand as the antibacterial one.
The point is to wash off microorganisms, not to kill them, so antimicrobial activity is really not necessary. So in the best case scenario, you probably just pay more for nothing. Worst case, you help the organisms become resistant.
If you really need to make sure, and you want to kill any “leftovers” on your hands (like I needed to when I worked at the pathogen lab at the university), you should wash your hands with NORMAL soap and THEN use alcohol.
Monika Wolaniuk, D.O. “How Does Soap Work?” https://www.hackensackmeridianhealth.org/HealthU/2020/08/11/how-does-soap-work/ published 11. august 2020, last accessed 6. february 2021
U.S. Food and Drug Administration “Antibacterial Soap? You Can Skip It, Use Plain Soap and Water” https://www.fda.gov/consumers/consumer-updates/antibacterial-soap-you-can-skip-it-use-plain-soap-and-water last accessed 6. february 2021
Jensen et al. (2017) “Quantifying the Effects of Water Temperature, Soap Volume, Lather Time, and Antimicrobial Soap as Variables in the Removal of Escherichia coli ATCC 11229 from Hands.” doi: https://doi.org/10.4315/0362-028X.JFP-16-370