Having received no response from the Irish Department of Justice, we made a phone call to the [honorary consulate of Ireland in Oman][1]. 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][2] 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 are planning to travel to Ireland in two weeks. I'll update this answer to reflect our experience. 

[1]: https://www.ireland.ie/en/dfa/embassies/#O
[2]: https://www.irishimmigration.ie/coming-to-visit-ireland/short-stay-visa-waiver-programme/