Welcome to the forum...Yes Irish water is safe to drink, we bottle it and send it all over the world so people can buy it... You may see signs in some "Eco friendly" places which advise against drinking the water from some taps as the water is recycled for washing bathing and flushing the toilet, these places also have a safe filtered tap.
__________________
Two rules for Ireland, Take your time & bring a sense of humour
There was a problem a few years back in Galway but all visitors were advised of the problem and provided with bottled water at their accommodations. Like any country, if work is being done on the water mains there may be a boil water alert in a certain area. Once again, it will be common knowledge.
Generally, Ireland's water is excellent. I usually get a bottle of water to keep in the car. When it is finished I fill it up with Irish water. The water does taste different from area to area. If you don't like the taste, get bottled. Sometimes the taps in your bathroom are fed from a holding tank where the water may have sat for some time. For drinking you may want to fill your bottle in the B&Bs kitchen instead (ask your hosts).
The water is safe. You won't get St. Patrick's revenge if you drink it.