No. New HIV diagnoses in the US are 67% male-to-male sexual contact, 22% heterosexual contact, and 7% injection drug use. (BTW, I have no agenda here except accurate statistics.)
According to [0] in 2020, MSM accounted for 71% of new HIV diagnoses, while people who inject drugs (PWID) accounted for 7% of new HIV infections. AFAIK similar stats are also for western and central Europe. These are population-level stats, not relative risks, but If we disregard PWID and scale to population size, MSM are still one to two orders of magnitude more at risk than non-MSM, non-PWID population, so they are clearly disproportionately affected.
In the developing world, it has nothing to do with promiscuity but lack of education and access to preventative measures like condoms and PrEP.