You're flogging a dead horse 🐎 with this. UK and Ireland sit within a regime called CTA (common travel area, which pre-dates EU and Schengen by decades) and every land, air and sea carrier is happy with photo ID. EXCEPT ryanair, who require a passport as ID. It's part of their condition of carriage and nothing to do with respective border controls. Just find anotheŕ carrier. Certainly do not waste your time and money pursuing legal recourse..