I don’t know what a “treat monster nature” is. I haven’t traveled much outside the core, so I can’t speak to this first-hand, but my impression is that most of the world is mostly a safe place to visit. There aren’t a lot of places that are going to punish you for renting hotel rooms and eating at restaurants as an American. Most people around the world know how to distinguish between America the empire and a civilian American spending money into the local economy.
I don’t think this concern is justified in most cases, but I’m not really in position to argue. If this were a common problem, I think I’d have heard about it, but outside of the occasional sensationalist news piece or Hollywood/TV thriller, I haven’t.
I do know an old joke, though: Before visiting a foreign country, it’s important to memorize three phrases in the local language: