Irish royalty are only those people who are principally considered royals of Ireland, not also those who have a claim to the Irish crown through the British crown. For instance, Victoria is not considered Irish royalty, even though she was in fact Queen of Ireland. Sitric Silkbeard would be considered an Irish monarch by virtue of being King of Dublin.

This is not a political statement, but merely an organisational one. It simply prevents recursion if we keep the constituent parts of the United Kingdom separate.