From my online research I have not found any precedents, but the decent character of the Irish nation leads me to think that they would be very responsible and accommodating.
According to published statistics, there were no refugee applications from US citizens in Ireland last year. Of note is that there were 70 rejected applications from South Africa, with none approved. I suspect it would be difficult to establish a case of US political persecution sufficient to justify refugee status. Despite the current political climate, the US simply does not reach the levels of depravity that countries such as Syria, Pakistan, Albania, etc can reach.