My opinion is that if basic hygiene is not keeping acne away then you need much more than a new soap. It's the hormones and your body reacting to them causing acne. AAS related acne needs to be treated from the inside out.
Non comedogenic soap, tea tree oil and shit like that are goboosterse but will not solve the issue.
Antibiotics, Accutane, and others I would look into.
I got hammered with acne this cycle and wasted a lot of money on products. Tried mega dosing B5 with zinc and pycnogenol too. Nothing helped. I am on Accutane now, 3 weeks in and I've cleared up over 50%. It's no joke though. Dry lips, nose bleeds and not having any oil on my skin feels odd. but It works.