I remember in yeshiva one day as a bris was about to start after minyan, someone came around and told everybody, "take off your tefilin!"
Recently I saw R' Moshe Feinstein explaining why we leave them on. R' Moshe writes (IIRC) that we don't have tefilin on shabbos because both are signs of the covenant, but circumcision is 24/7 so by nature it's non-exclusive, and in fact it is therefore appropriate to keep tefillin on at a Bris.
(I'm talking here about the ordinary people watching in shul. I certainly understand why the father, mohel, and sandek would have theirs off, as they're busy dealing with a baby!)
So which is it? On or off? Why? Is R' Moshe differing with some well-known posek here, or common practice?