Did the old world have gonorrhea, herpes, genital warts, molluscum, trich, or any other visible STD? It seems like any one of those would be sufficient to cause a superstitious, iron age people to suspect something was plaguing the sexually promiscuous.
Notably, when syphilis was introduced into the Old World population, it was described as a very severe acute disease. It only became more chronic after a period of adaptation that took several decades. This might have made the initial societal reaction more extreme.
https://www.everydayhealth.com/syphilis/painful-history-odd-...
Chlamydia rarely has life threatening complications but gonorrhea and hepatitis can kill. And there aren’t any STDs that don’t often cause infertility. Religions favored not screwing around because you’re guaranteed to get an STD eventually if you do, and that will very likely lead to infertility or worse.
Much more likely, the problems with promiscuity were related to 'bastard' children and their role in inheritance; and to the father's uncertainty that a child was biologically theirs. In addition, many religious outlooks favor abstinence from bodily pleasures of all kind, so forbidding sexual pleasure and especially promiscuity seems well in tone with this.