At our parish, non-Catholic Christians who attend Mass every week with their (Catholic) families have been allowed to become regular readers (as in: bidding prayers, first and second readings, psalms) in the general rota. All readers are required to receive training and are vetted by the priest, to make sure they approach it in a properly reverential manner.
I know that the priest consciously made a decision to allow these particular people to become readers, even though they are not Catholic: it isn’t an oversight. This priest has generally impressed me with his orthodoxy, charity, understanding of the faith, and enthusiasm for the liturgy. I assumed that this sort of decision was within his pastoral remit. Mark’s quote seems to suggest that isn’t the case, so I wonder if there is more written about this than just that document.
In particular, I believe the priest’s decision was informed by the fact that these people attend Mass every week with their Catholic families, contribute to parish life, and so fall within the parish even while not being in full communion with the Church. They approach Scripture with reverence, and do not receive Communion. They are not reading as representatives of another church, and if you didn’t know them personally you wouldn’t know they weren’t Catholic. I wonder if the Directory for the Application of
Principles and Norms on Ecumenism is dealing with a more “Churches Together” sort of thing, rather than the more pastoral situation?