Check out /r/ShitAmericansSay sometime. It's mostly 'salty Europeans' shitting on Americans very often for celebrating their heritage (although to be often a lot of those posts the Americans are being pretty stupid). The comments and a lot of other posts seem to suggest they actually feel Americans should shut up about 1/2, 1/4, 1/8, etc. and shouldn't celebrate their ancestry. I remember seeing people say Americans shouldn't identify this way if they don't even know what part of the country their ancestors are from. Since most of the Americans like this have been here since the early 20th century or before, this kind of information requires some actual research which costs money. Overall, this kind of thinking comes from some ignorance and difficulty in understanding what it means to be this kind of American.

But yeah I've lived throughout Europe and a lot of people have asked about what I know of my ancestors and heritage with genuine interest, especially when we're 'compatriots,' but that's probably also because people are typically nice.