Keep the status quo.
The first suggestion on the ballot paper is to merge the state and island articles into one (option A.) This would not only reverse the usual policy in WP:SPLIT, it would merge two articles into one even though they obviously deal with different topics.
As the Irish Government’s own website puts it: “The Republic of Ireland occupies 70,282 sq. km. of the island of Ireland which has a total area of 84,421 sq. km.” Thus the state and island are clearly not the same thing and require disambiguation. The Irish Government’s official tourist website also makes this clear: “The island of Ireland is made up of the Republic of Ireland (a sovereign state of its own) and Northern Ireland, which is a dominion of the United Kingdom.”
Another suggestion (option B) has been made to reverse the order of the articles with the state taking the name Ireland. However since the state is a subsection of the island, it makes sense for the island to have the name rather than the state, otherwise we end up with fallacies like "Belfast is not in Ireland." These arguments have often centred on the fact that 'Ireland is the official name of the state and should therefore have the article title.' Yet there are a large number of articles on Wikipedia which do not use the official country name for example Latvia while others are known by alternate names e.g. Burma.
Ireland (state) has been one suggested compromise and while this would meet our naming conventions it suffers from the problem that English speaking countries such as Australia and USA use the term "state" to refer to a unit of local government.
Having Ireland as a disambiguation page is a possibility (ballot options C and E.) Arguments have been advanced against this usually on the grounds that it receives less page traffic than the articles about the state and the island. I'm not convinced by the "page traffic" argument since it overlooks the fact that page traffic is influenced by internal wikilinks. The number of actual article pages that link to the current Ireland disambiguation page appears to be less than 20, whereas the island and state pages have over 500 article pages linking to them.
Numerous attempts have been made over the past two years to move the Republic of Ireland (ROI) article to Ireland, Ireland (state) or some such variation. All of these have not only failed to gain consensus, they have usually shown the majority of users in favour of the status quo. For example this poll, one of the most recent showed 75% in favour of retaining the article at Republic of Ireland.
One of the most common arguments against the use of Republic of Ireland has been some alleged anti-Irishness in the term, though no sources have been produced to back up this dubious view. The term was actually one created by the ROI government in the Republic of Ireland Act 1948.
To show that it is a widely used and NPOV term I would also draw attention to the following:
Given this usage both within and outside Ireland, I see no compelling argument to move the pages from their current locations.