Having received no response from the Irish Department of Justice, we made a phone call to the honorary consulate of Ireland in Oman. Here's what we established:
- It is legal for Omani citizens to enter Ireland from the UK with just an ETA. Many Omani people have successfully travelled to Ireland in this manner.
- Airport personnel may not be aware of your right to travel to Ireland. If you face issues with airport staff, show them a printed document confirming your right to travel.
- The consulate is not permitted to issue written statements confirming your right to travel. We were told that it's sufficient to provide a screenshot of an online source (e.g. the website of the Department of Justice linked in the question).
- No Omani citizens have been refused entry to Ireland on the basis of an ETA that the consulate knows of.
- We were advised to travel via the London Heathrow airport because the check-in agents there are familiar with the travel rules for Omani citizens.
You will face difficulties at check-in
Against our better judgement, we disregarded the consulate's advice and decided to travel via Liverpool. My Omani companion was denied boarding at check-in. We tried to explain our situation, but the check-in agent insisted that Omani citizens need a visa to travel to Ireland.
Ultimately, the check-in crew advised us to book a flight to Belfast and to enter the Republic of Ireland by land. We did so, and we travelled home via the same route.