The phrase "genital mutilation" elicits sentiments of revulsion and sympathetic pain. "Circumcision" usually doesn't. Why not? They describe the same thing, at least when performed on non-consenting infants or children. Let's put aside distinctions of connotative and denotative language for the moment to posit an alternate reality in which people had never cottoned to the idea that cutting implements have no business being in the vicinity of the organs of generation.
Description of the alternate world-state:
Here, the practices of clitoral excision, labial amputation, castration and penile circumcision were never ever introduced. The very notion of putting sharp steel anywhere near the crotch region would be simply baffling. Such practices were not even in the set of activities under consideration.
I suggest to you that under such an arrangement, the practice of circumcision would be morally equivalent to the various acts of female genital mutilation. Yes, the medical and sexual outcomes would still be widely disparate, but the idea that the agent (the parents, the tribe, the church, [the state?]) has some justification to make an irrevocable decision over the disposition of body parts for cosmetic* purposes would strike people as monstrous.
Because circumcision is emphatically not regarded as monstrous by most people, there must be some curious moral intuition at play. Some of it to be sure is ex post justification, some of it is cultural inertia. I'd reckon a fair chunk is just that people probably don't think carefully about the implications of the practice itself. It's sanctioned (somehow) and that's enough justification to make it hunky-dory.
On the EE of circumcision, with regard to infants there is unquestionable coercion by human agency. In the case of rites of passage, there might be an admixture of coercion by human agency and circumstance: sure, you can forego the rite, but you'll never be considered a man or a real part of the tribe. What kind of BATNA is that? How about at the standard age of majority? Empirically speaking, do many men undergo elective surgery? My priors tell me no, but I'm insufficiently familiar with the medical literature to make informed claims. Does a lack of voluntary circumcisions imply anything about the nature of ex post regret or have any bearing on the moral legitimacy of circumcision? From behind the veils of uncertainty and ignorance, what would be the proper moral intuitions about circumcision? What's the BATNA?
*I acknowledge that the institutions of genital mutilation may serve certain institutional functions, but since this discussion is focused primarily on circumcision in the secular West, I argue that the repeated-game Nash equilibrium position in favor of the practice is not especially relevant. If any of my half-dozen or so readers are interested in more on the subject, either comment below or e-mail me and I would be happy to do a follow-up post on the topic.