People said funny stuff like this when I was a child, especially on St. Patrick's Day. It was nicer than, "Go back to China!" which others spat out. When you're told things like this you might feel a little different, isolated, even alienated. You could become a person who thinks they don't belong.
I like to remember what the poet Audre Lorde warned us: if we don't "define ourselves for ourselves we will be crushed into other people's fantasies for us and eaten alive." Maybe I didn't look it or act it but I knew I was Irish as my paternal grandparents were born and raised there and fled the old country with stories of famine and colonization.
It became important for me to declare that "I, too, am America," in the words of Langston Hughes. This means asserting my own and others' belonging when I hear political leaders describe immigrants in unhuman terms. And when I see our leaders inflicting immense suffering on innocent people I'm called to take on a citizens' responsibilities of breaking my silences by speaking from the burnings of my heart and asking others to do the same.