First and most important: If this is in reference to a particular and/or individual situation, please confer with your Rabbi to receive the most authoritative guidance for you. However, for the sake of general discussion and edification, here is my response:
One’s obligation to perform brit milah on the eighth day supersedes many mitzvot, including Shabbat. If a child is scheduled to be circumcised on the eighth day of life, and there happens to be an intervening death and funeral, the brit milah still happens on the eighth day. The rituals of the brit milah – the circumcision itself, the roles of father and mother, sandek, k’vaterin, etc – must be performed as needed, but see below regarding the state of mind and the meal that follows.
One may defer a brit milah but only for medical purposes. In that vein, the higher mitzvah, of course, is pikuach nefesh – the preserving of life – and therefore if the child is not ready for circumcision, then it is deferred until his doctor declares him fit.
The question about which authorities have ruled is whether one can “celebrate” the brit milah, which is understood to be attending the meal that follows. If the brit milah happens to be scheduled for the day of the funeral or the period of shivah – the first seven days of mourning after the burial – it is recommended that a mourner not attend the meal of celebration of the brit milah even though s/he may (some may say ‘should’) attend the circumcision ceremony.
So to review, the celebration is something that is deferred until after shloshim – the thirty day period of mourning – but the brit milah goes as scheduled on the eighth day, even including the parents, mohel, and others involved in it.