The government of Ireland at the time was highly nationalistic, and hated Britain for historical injustices inflicted on the Irish.
Ireland actually supported Germany in the beginning for historical reasons, so I'm not sure if our forces would have been welcomed there initially, but what could they do about it? And most likely we would have gone to Northern Ireland anyway, still in Britain's control. Hitler wouldn't have had time to get in there, his hands would have been too full in Britain.