The biggest difference is that we're several generations removed from the time where Irish-Americans have suffered any sort of serious discrimination. That's not the case for blacks, Asian-Americans, Latinos or Native Americans. If you see a frat party making fun of your culture, and you and your family still suffer from discrimination on a day-to-day basis, you were called "dirty Mexican" and "spic" in elementary school, people made fun of your accent (or, if you didn't have an accent, told you that you spoke remarkably good English for your race
), employees followed you in stores to make sure you weren't stealing, cashiers don't touch your hand when they give you money as if you were dirty, people claim you only got into college because of affirmative action, blah blah blah, I could go on -- that's going to be a whole hell of a lot more hurtful and open more wounds than if you see a frat party making fun of your culture and 100 years ago your great grandfather was denied jobs and called whatever it is that they used as a derogatory term for Irish back then.
Irish-Americans today don't know what it's like to face discrimination for their race because they aren't discriminated against anymore (not in any significant way, at least. There will always be the random crazies who hate the Irish or the Polish or the Germans for some made-up reason that they deem suitable). American people of color do and are. It's not a double standard because you're comparing two completely different situations.