I have never taken hiking boots to Ireland. If you want to do heavy duty hiking then take some. If it is just general sightseeing you most likely not need them.
Hi Marie, We actually wished we had wellies last May when we there, though it was an unusually wet Spring. Still, we did do hiking and waterproof hikers were great to have. As Michele said, if you'll be doing general site seeing and well-travelled paths, you shouldn't need to worry about lugging them over.