I haven't used soap in the shower for at least five years. Only when cleaning hands, and I do use antiperspirant) I just scrub myself with my hands in the shower top to bottom. (I am bald tho).
No one has ever mentioned me smelling bad, even my current co-workers who do say it if someone is smelling.
What kind of antiperspirant are you using that doesn’t require soap to remove it? They almost always have a residue that keeps them in place that doesn’t normally just wash off.
I had a long time of issues with my skin, and when I researched for causes I realised I was using too much soap. So I switched to soap every other day, once a week and eventually just dropped soap altogether when I found I didn't really need it. Haven't had any issues with my skin since.
I love how people say this. Dude, other people will not tell you if you smell bad unless you ask fairly insistently. It’s awkward, and people would just rather ignore it than broach that awkwardness. Tell someone you work with and trust everything you have just written here, and see what they say. My bet is either you are “that smelly guy at the office” or “meh you smell kinda funky, but it’s not horrendous”. Either way: wash ya ayyssssss
My brother, I work in a kitchen. The people there do, (and have) told their fellow workers when they smell. Either when they don't shower enough, or when they use too much deodorant.