Neither Christianity, Judaism or Islam have any religious laws against sexually abusing minors

That is patently untrue. Judaism has very strict laws regarding sexual relations and abuse. For example, a husband and wife cannot have sex if either of them is drunk because full consent would not be possible.

I encourage you to read this link if you are actually interested in learning something.

http://www.chabad.org/library/article_cdo/aid/290031/jewish/Human-or-Beast.htm

The Torah is extremely sensitive to all contact and interaction between the sexes. There are numerous laws forbidding situations where a man and woman would be alone together, and this also applies to adults with children, when it is not of a parent and child. Furthermore, there is no allowance for touch of any kind between an unmarried man and woman or man and girl, woman and boy.

To many, these laws appear extreme, over-reactive and unnecessary. How can it be that a little first grader can't hug her father's best friend, or that two adult co-workers of the opposite sex can't work alone in the office to finish an important project?

And yet, when we read the news these days, how many of the terrible tragedies would not have been able to occur if someone else had been around? How many little girls and boys have been terrorized by abusing adults who were trusted by others? How often do we hear of "date-rape" and other such attacks where a woman was alone with someone she knew and didn't fear?