The infallibility (or lack thereof) that can be attributed to priesthood leaders is not different from that which can be attributed to scientists or any other community that pretends to cultural authority. (This would include political parties, activist groups, nations, ethnic minorities, social identities, etc.) In both cases, the party in question fully acknowledges that they are imperfect and completely open to critical review. Neither party claims absolute and unyielding certainty.
While each community is open to critical review of its imperfect claims, they also insist, however, that such critical review must come from WITHIN their own community – through processes that they recognize as legitimate. This inevitably places the community beyond the scope of “outside” criticism. Indeed, within our modern, liberal society such communities will tend to moralize any such external criticism as an illegitimate or oppressive interference with their autonomy or academic/religious freedom within their “rightful” stewardship or domain. (Non-modern moralize such interference in different moral terms – moral pollution, etc.) Each community is thus fully open to correction, but only through the rules, means, techniques, values, persons and truths that define, structure and differentiate it from other communities.
Each community will, for obvious reasons, self-describe their own unresponsiveness to outside criticism in much softer terms that I have used. Such communities will often claim to be fully open to a “true” version of other competing communities. Such claims, however, are means of retaining exclusive rights over the contested domain rather than an inclusive sharing of these privileges. Even within Popper’s idealistic depiction of science as an open society – in stark contrast to Kuhn’s closed society – any person can call scientists’ claims into question but only through the properly “scientific” means and techniques that have already pre-defined the community. Thus, scientists do not place themselves open to correction from prophets to the extent that the latter are not fellow scientists nor do prophets from scientists to the extent that these are not prophets.
For better or worse, the infallibility of priesthood leaders exactly parallels that of scientists. Whether one perceives infallibility in one community rather than the other depends largely upon whether one is looking at it from the inside or outside of that particular community. Each community is only perceived as (practically) infallible to the extent that it is (practically) unresponsive or open to correction through some means or rules of correction that are themselves native to some other community. In this way, the very same unresponsiveness to outside criticism that is moralized as “autonomy” from within a community is similarly moralized as “infallibility” from outside that community. Stated differently, the outsiders’ “fallibility” is practically equivalent to the insiders’ “heteronomy”.
Whichever of these narratives feels more intuitive to any person will depend less upon the facts of the case at hand and more upon the extent to which they have internalized the rules and values of the community in question.