The difference between regular soap and antibacterial soap is that the antibacterial agent is usually something like triclosan or triclocarban, which is meant to slow the growth of new bacteria.
This gives soap a 1 2 punch as when you wash you kill pretty much 100% of the bacteria, but bacteria is everywhere so you almost immediately start picking more up as soon as you start coming into contact with other surfaces (the shower knob, the door handle, your phone, etc) so the antibacterial agent will help prevent the explosive bacterial growth after you’ve acquired it.
To be clear, I’m not defending antibacterial soap. In 99% of cases regular soap does exactly what people need. As a regular person, if you’re worried about bacterial contamination that much, you shouldn’t be using antibacterial soap in place of regular soap when you wash - you should just be washing more often.
I personally do have a very specific benefit that I experience when I use antibacterial soap: it takes longer for me to start smelling after I start sweating. The difference is noticeable for me. Presumably it is noticeable for the people around me as well. I could fix this problem by showering more often, but when I already shower once a day I’m not gonna go grab a quick one after lunch just for the hell of it, especially since excess water use is a problem anyways. Also where the fuck am I gonna find a shower that I’m just free to use at lunch time? So, antibacterial soap, and deodorant, fills that time gap for me.