I think the history of circumcision provides an important insight on this topic.
The non-religious history of circumcision started in England at the end of the 1800s and became very popular in English-speaking countries between 1920 and 1950. England introduced this procedure to the U.S. However, the practice declined sharply in the United Kingdom after the Second World War, and a bit later in Canada, Australia and New Zealand.
Routine infant circumcision has now been abandoned in New Zealand and Britain, and is much less common in Australia and in Canada.
In Britain, it was after a decision was taken by the National Health Service (NHS) in 1949 to not cover the procedure that there was a marked decline in circumcision. This decision was based on an influential article by Douglas Gardiner "The Fate of the Foreskin" claiming that circumcision resulted in the deaths of about 16 children under 5 each year in the United Kingdom (a rate of about 1 per 6000 circumcisions).
In Canada, Individual provincial heath insurance plans began delisting non-therapeutic circumcision in the 1980s. It resulted in infant circumcision rates falling from roughly 50% in the 1970s to its present value of 11%, with strong regional variations.
Today, none of the major medical societies in the USA, Britain, Canada, Australia and New Zealand recommend routine non-therapeutic infant circumcision. Major medical organizations in the USA and Canada say that parents should decide what is in their son's best interests, refusing to make a recommendation one way or another. The AAP (American Academy of Pediatrics) advises that "Physicians counseling families concerning this decision should assist the parents by explaining the potential benefits and risks and by ensuring that they understand that circumcision is an elective procedure."
A remedy against masturbation
When circumcision was introduced, it was believed that masturbation caused a lot of different illnesses. It was considered extremely immoral and many children, both male and female, have been circumcised through the years because parents found them "in the act."
It was already known at the end of the 1800s that the removal of the foreskin, which is the only moveable part of the penis would reduce sexual sensitivity and restrict movement of the penile shaft.
It was believed that masturbation caused blindness, mental illness, alcoholism, epilepsy and several other ills. It therefore made sense to some physicians that circumcision would stop masturbation and prevent the onset of these illnesses.
Here is an interesting quote from Dr John Harvey Kellogg (yes, the Kellogg from the famous Corn Flakes!):
"A remedy [for masturbation] which is almost always successful in small boys is circumcision...The operation should be performed by a surgeon without administering an anesthetic, as the brief pain attending the operation will have a salutary effect upon the mind... In females, the author has found the application of pure carbolic acid to the clitoris an excellent means of allaying the abnormal excitement."
Here is another quote from Karen Erickson Paige (an anthropologist) from her book The Ritual of Circumcision written in 1978:
"In the 1890s, it became a popular technique to prevent, or cure, masturbatory insanity. In 1891 the president of the Royal College of Surgeons of England published On Circumcision as Preventive of Masturbation, and two years later another British doctor wrote Circumcision: Its Advantages and How to Perform It, which listed the reasons for removing the 'vestigial' prepuce. Evidently the foreskin could cause 'nocturnal incontinence,' hysteria, epilepsy, and irritation that might 'give rise to erotic stimulation and, consequently, masturbation.' Another physician, P.C. Remondino, added that 'circumcision is like a substantial and well-secured life annuity... it insures better health, greater capacity for labor, longer life, less nervousness, sickness, loss of time, and less doctor bills.' No wonder it became a popular remedy."
When it was finally realized that masturbation did not cause illnesses, the foreskin got blamed for penile and cervical cancers, urinary tract infections and sexually transmitted diseases.
I believe that relating the non-religious history of circumcision is important in understanding why the procedure came to be. I believe that this understanding will help parents make an informed decision for their son.