Don't fret, but also don't yell
In general, Chileans are comfortable with Americans. Never over the course of my nearly four months in the country did I receive any backlash as a result of being American. Occasionally, Chileans would criticize US government actions in conversation, but all that I conversed with understood the distinction between the beliefs of an individual and the beliefs of that person's government. Following Barack Obama's election, I was personally congratulated multiple times by Chileans (including random ones on the street). To be well-received, the most obvious suggestion I have is to not speak in the infamous loud English that American tourists tend to speak in when abroad (or at home). Keep your voice at a reasonable level like everyone else on the street, and you'll reduce the chance of attracting any unwanted attention (the little that there is).