Angel from the Altar:
You may banish up to X evil cards from a discard pile or you may exchange a good card from hand with a good card from Reserve. Cannot be negated if The Golden Altar is in play.
Noah:
You may exchange a card in hand or territory with a human of matching brigade (or 2 flood survivors) in deck or discard pile. May band to a flood survivor. Cannot be interrupted.
All abilities that target hand have an implied reveal ability, where if the holder of the targeted hand cannot complete an action required by another ability or game rule, they must reveal that hand. For example, if a card requires a player to underdeck two good cards from hand, they must reveal their hand if they can underdeck zero or only one. If they can underdeck both and satisfy the requirement, there is no reveal.
If a search ability targets a specific type of card, reveal the targeted card before performing any other action with that card.
Do you have to reveal the card you exchange from hand with Angel from the Altar or Noah? The REG entry on Reveal is about being unable to complete the action, not showing that you meet the requirements for the action. The one on Search definitely applies to what you exchange for, but not necessarily the other end.
I think they should be revealed, but I don't see the rule to back it up.