Irish citizens travelling to countries other than the UK must be in possession of a valid passport, and visa if appropriate, to obtain entry. Airlines operating services to these countries may verify that passengers comply with this requirement before departure.
In the case of travel to the UK, there has been no change in the position that Irish citizens do not require a passport for immigration purposes. I understand, however, that at least one airline which operates a ticketless booking service, requires that persons other than children under 16 years of age present a photo identification document, which could be a valid passport, driving licence with photograph, international student identity card with photograph, at check-in to confirm that their identity matches the reservations made.