It is a mistake to file objection to circumcision as something that happens to Jewish practice from outside. A small but articulate current of Jewish objection to it is old, and the contemporary version is not imported.
The alternative that has developed is a naming ceremony without cutting, sometimes called brit shalom, performed by a small number of rabbis mostly in the Reconstructionist and Humanistic movements and by unaffiliated celebrants. Its advocates argue that the covenant is carried by observance and by belonging rather than by a surgical mark, and that a tradition which has repeatedly reinterpreted its commandments can reinterpret this one. Organised Jewish groups opposing circumcision exist in the United States, Israel and Europe.
The response from the mainstream of every major Jewish denomination, including the liberal ones, has been firm. Reform Judaism, which dropped a great deal else, reaffirmed circumcision and trains its own circumcisers. The argument made against brit shalom is not primarily medical. It is that this particular commandment has been the one Jews were killed for keeping, twice under empires that specifically banned it, and that abandoning it under pressure from a surrounding society is a category of act with a long and unhappy history.
That argument is doing real work and it is worth stating precisely rather than dismissing. It is also not an answer to the objection actually raised, which is about the consent of the person being cut rather than about the strength of the tradition. Both things are true at once, and the entries on this site are not going to pretend otherwise in either direction.
The parallel Muslim debate is smaller and differently shaped, largely because khitan has no fixed day, no unanimous legal status, and no comparable history of prohibition to defend against.