Answer:
Speaking for myself and a few close friends we tend to just go "meh". If someone's parents were both Irish then that's not too bad or even their granparents, what is a pain is when Americans say "oh my great grandmother on my fathers side was Irish, so im Irish too" and despite their claim to be Irish couldn't even tell you that Ireland is in Europe, that kind of statement tends to drive some of us crazy. But people who actually know somthing about Ireland and have strong links to the people over here are fine, i don't mind calling them as Irish-American since their not ignorant of the culture of Ireland and are American so hence Irish American. Just my 2 cents.