My opponent says I cannot respond to his Priest of Forgotten Gods sacrificing two creatures. He states that his "tap, Sacrifice two other creatures" cannot be responded to like Altar of Dementia, but I'm arguing that it's different. Altar of Dementia is specifically cost:effect, not tap, cost:effect. I tried to cast Unsummon on one of the two creatures he's trying to sacrifice to make his activated ability illegal. I had a difficult time searching for a ruling specific to this card.
The activated ability of Priest of Forgotten Gods is no different from that of Altar of Dementia in this respect.
In both cases, sacrificing creatures appears as part of the cost to activate the ability (for the former, "T, Sacrifice two other creatures", and for the latter, "Sacrifice a creature") (C.R. 601.2, 601.2a). (Remember that an activated ability's cost is "everything before the colon" [C.R. 601.2a].) And in both cases, while the ability is being activated, players don't have priority to cast spells (including spells that would remove creatures from the battlefield) (C.R. 601.2a-i and 602.2a-b have no priority window until the spell is cast or ability activated; C.R. 116.1a-b).
In both cases, sacrificing creatures appears as part of the cost to activate the ability (for the former, "T, Sacrifice two other creatures", and for the latter, "Sacrifice a creature") (C.R. 601.2, 601.2a). (Remember that an activated ability's cost is "everything before the colon" [C.R. 601.2a].) And in both cases, while the ability is being activated, players don't have priority to cast spells (including spells that would remove creatures from the battlefield) (C.R. 601.2a-i and 602.2a-b have no priority window until the spell is cast or ability activated; C.R. 116.1a-b).
See also this thread, this thread, and this thread.