January 31, 2019
One of the medical benefits of newborn circumcision is a lower lifetime risk of penile cancer. A secondary benefit is a lower risk of cervical cancer for female sexual partners. In an attempt to nullify these benefits, circumcision opponents have referred to the American Cancer Society, implying that the respected health organization has declared that the procedure has no protective benefits against cancer.
Intactivists have cited a 1996 letter sent by two doctors to the American Academy of Pediatrics.  Intactivists quote the following statement from the letter:
"As representatives of the American Cancer Society, we would like to discourage the American Academy of Pediatrics from promoting routine circumcision as a preventative measure for penile or cervical cancer. The American Cancer Society does not consider routine circumcision to be a valid or effective measure to prevent such cancers..."
First we'll take a look at what the American Cancer Society actually says about circumcision. Then we'll examine the controversial letter.
What does the American Cancer Society say about circumcision?
Several pages on the ACS website address penile cancer, two of which discuss the potential benefits of circumcision. The following are quotes from these pages.
Risk Factors for Penile Cancer
NOT BEING CIRCUMCISED - Men who were circumcised as children may have a much lower chance of getting penile cancer than those who were not. In fact, some experts say that circumcision as an infant prevents this cancer. The same protective effect is not seen if circumcision is done as an adult.
PHIMOSIS - Penile cancer is more common in men with phimosis. The reason for this is not clear, but it might be related to the build-up of smegma or from inflammation that results from phimosis.
SMEGMA - Smegma is more common in men with phimosis, but can occur in anyone with a foreskin if the foreskin isn't retracted regularly to clean the head of the penis... Most experts now believe that smegma itself probably doesn’t cause penile cancer. But it can irritate and inflame the penis, which can increase the risk of cancer. It might also make it harder to see very early cancers.
HUMAN PAPILLMAVIRUS (HPV) INFECTION - Infection with some types of HPV appears to be an important risk factor for penile cancer. In fact, HPV is found in about half of all penile cancers... Men who are not circumcised may be more likely to get and stay infected with HPV. 
Can Penile Cancer Be Prevented
Circumcision - In the past circumcision ... was suggested as a way to lower penile cancer risk. This was based on studies that reported much lower penile cancer rates among circumcised men than among uncircumcised men. But in some studies, the protective effort of circumcision wasn't seen after factors like smegma and phimosis were taken into account. Still, some experts have said that circumcision prevents penile cancer. In the US, the risk of penile cancer is low even among uncircumcised men. Men who aren't circumcised can help lower their risk of penile cancer by practicing good genital hygiene. 
In other words, the American Cancer Society advises that males have a low risk of penile cancer, and circumcision during infancy can reduce the risk even further. And circumcision reduces the risk for some other conditions that are risk factors for penile cancer.
Although the ACS website doesn't mention circumcision specifically with respect to cervical cancer, HPV is identified as "the most important risk factor for cervical cancer."  As stated above, uncircumcised men have a higher likelihood of acquiring and retaining HPV; thus they are more likely to infect sexual partners.
This information is consistent with the 2012 AAP Technical Report, which considered a study "that found a protective effect of male circumcision against cervical cancer in the female partner(s) of men who have multiple female partners."  And the Mayo Clinic, the #1 highest ranked hospital in the United States,  affirms that "cervical cancer is less common in the female sexual partners of circumcised men." 
Letter contains personal opinions of former employees
Now what about that 1996 letter? It turns out that the two doctors who wrote the letter were not authorized to speak on behalf of the American Cancer Society. They were not even current ACS employees, and they did not convey official ACS policy. In fact the ACS did not - and still does not - have a formal position statement on circumcision.
In response to inquiries about the letter, in 1998 the ACS explained that:
A two year-old letter being circulated on the Net discussing scientific evidence regarding penile cancer and its relationship to circumcision is personal correspondence reflecting the observations of two former ACS staff members. The American Cancer Society does not have a formal guideline statement on circumcision. 
It should be noted that even the premise of the letter - that the AAP promotes routine circumcision - is misleading. The AAP doesn't promote routine circumcision, but rather supports each parent's right to choose whether or not to circumcise her infant son. 
How many circumcisions are needed to prevent penile cancer?
In addition to the illegitimate letter, intactivists also point to a genuine ACS statement. The health organization said that "it would take over 900 circumcisions to prevent one case of penile cancer" in the United States. 
But that statistic has little relevance to a parent considering whether to have her son snipped. First, penile cancer prevention is just one of several medical benefits. The procedure also reduces the lifetime risk of urinary tract infections, phimosis, balanitis, and sexually transmitted diseases. And circumcision can make male hygiene easier. While parents may choose circumcision for the collective health benefits, few if any authorize the procedure solely for penile cancer prevention.
Second, the low risk is of no comfort to those affected by the disease. Consider the tragic case of Dale Clarke, a talented British soccer player. In 2017 Clarke was diagnosed with penile cancer. Ten months later he was dead at the age of 26. The rare nature of the disease won't provide comfort to his parents, his siblings, his fiancée, his 6 year-old son, and his daughter who was born six weeks after his death.  Statistically speaking, if Clarke had been circumcised in infancy, it's almost certain he would be alive today.
Finally, with all due respect to the American Cancer Society, it's a misuse of the risk factor to say that 900 boys need to be circumcised to prevent one case of penile cancer. A parent only needs one boy circumcised in order to protect her son.
 Hugh Shingleton, M.D. and Clark W Heath Jr. M.D.; letter to Dr. Peter Rappo; February 16, 1996; reprinted by CIRP. - Circumcision Information and Resources Pages.
 "Risk Factors for Penile Cancer"; American Cancer Society; Last Revised: June 25,2018
 "Can Penile Cancer Be Prevented"; American Cancer Society; Last Revised: October 19, 2017
 "What Are the Risk Factors for Cervical Cancer"; American Cancer Society; Last Revised: November 1, 2017
 Susan Blank M.D. et al: Male Circumcision Technical Report; Pediatrics; September 2012
 About Us - Top Ranked; Mayo Clinic; "In the U.S. News & World Report rankings of top hospitals, Mayo Clinic is the No.1 hospital overall and No.1 in more specialties than any other hospital in the nation."
 Mayo Clinic Staff; Patient Care & Health Information - Circumcision (male); Mayo Clinic
 "Dispelling Miscommunications"; ACS News Today, Atlanta, 1998; reprinted by CIRP
 Susan Blank M.D. et.al.; American Academy of Pediatrics Circumcision Policy Statement; Pediatrics; September, 2012
 "About Penile Cancer"; American Cancer Society; 2016. (We suspect that Your Whole Baby included the American Cancer Society website on its meme without ACS approval.)
 Intactivists dismiss the value of lowering the risk for penile cancer by pointing to the rarity of the disease. And yet intactivists also cite a risk of death as a reason not to circumcise, despite the fact that many more Americans die from penile cancer than from infant circumcision. Less than one boy per year - less than 1 in 1.3 million - dies from a neonatal circumcision in the United States. By contrast the ACS estimates 380 American men died of penile cancer in 2018.
 Alexander Robertson, "Talented footballer, 26, due to become father for second time succumbs to penis cancer"; Daily Mail Online; May 10, 2018