As a tourist myself, I'm aware that I'll fatally be recognized as one as soon as I open my mouth -doesn't matter how well I speak the local language, people will always notice. So, in practical terms, I don't think it's possible to blend in to the point of people not realizing you're a foreigner.
What I mean by "blending in" doesn't equal "hiding your nationality at all costs". It's simply not to be recognized as a tourist a mile off, or at the first glance; this is not that hard, you don't need to
immerse deeply -a little research about the culture and history of the place you're visiting and learning a bit about the local dressing code will sufice. And of course, avoid being loud when in big groups.
I wouldn't say that not blending is
wrong. Personally, I think it's a sort of commom sense and a sign of politeness and courtesy (when in Rome...
), the same way you adapt when visiting someone who has different habits than you and your family. Of course, if you don't mind contacting locals and your plan is following your travel guide and go back home, then blending in doesn't sound like a must-do, but still.
I like to keep in mind that no country is obligued to let me into their territory, they can turn me down upon my arrival at the airport just because -and still I was alowed to be there. It may sound a bit naïve, but well, as for myself, I think being nice is the right thing to be done.
Either way, in the particular case of American tourists, in Europe at least, they are sometimes seen as quite the brash people, so being loud and too outstanding may come across as rude, even offensive. Sometimes, blending in is even a question of safety, it will at least spare you from becoming an easy target to thieves in big cities -and maybe even to terrorists.