There is no proven data showing a link between the availability of historical and genealogy information on government websites and identity theft. The comments of Data Commissioner Hawkes calling the data a "treasure trove for people of evil intent" and a "very shocking" example of a public service failure are alarmist and misleading.
Irish citizens should ask that their government representatives have a reasonable dialogue on the issues and separate rhetoric from the facts. There are practical controls that can be put into place, on the persons who are able to access the information, to the ranges of available data in the Civil Records search.
In May 2014, the Federation of Genealogical Societies Records Preservation and Access Committee launched a Genealogists Declaration of Rights. The issues raised in Ireland touch on similar concerns for a balancing of access to information and privacy. While the Declaration of Rights is aimed at the US, the statements could easily apply to other locations.
Disclaimer - these views are my own. I have Irish ancestors on at least two branches of my family tree, one left Ireland around 1805 and the other arrived in the US by at least 1860. I have not made use of the information and resources of Irishgenealogy.ie, and until this story appeared in my newsfeed on Monday, I was not familiar with them. But I might want to make use of their services in the future, especially if AHG makes earlier historical data available. I am also not a specialist in Irish data protection law.