JohnG has said much more sensitively what I meant, which is that "American tourist" is a stereotype, not a description. Sensitive, tactful and genuinely interested American visitors are always welcome. But for decades there have been substantial numbers of a type of tourist from the USA who inhabits the opposite end of the spectrum.

These "American tourists" talk loudly, they couldn't care where they are, who the locals are or what anyone's sensitivities are. They appear never to have heard of the words "please" or "thank you", or the phrases "may I have" or "I would like". They often throw money around with condescension. They are too keen to let everyone know where they come from. They behave as if they are from the best country in the world, and are deigning to set foot in an inferior place. (You can understand why locals might object to that attitude.)

These are the people who have created the sterotype. It is the stereotype which is passionately loathed in London and across Europe (and most of the rest of the world), and, for that matter, is also seen as easy meat for the ripoff artists who are in every tourist hotspot in the world.

To get back to your original question, what I meant was that if you don't dress in a stereotypical fashion, people will not immediately assume that you are a stereotypical "American tourist" and adopt prejudiced attitudes towards you. It gives you a chance to be taken on your own terms, as yourself. That's how you will be doing yourself a favour.

I'm sorry if I sound a bit extreme on this, but I have grown up and lived in one tourist hotspot after another all my life, in different countries in the world. As a result, one of the best small pleasures I get when visiting a place I am enjoying is when I get asked "So how long have you lived here?"