It is true that the sentiment against tourists rising local rent prices is not only against Americans. @Vegas_Millennial mentions NYC, but also San Francisco, LA and Honolulu have legislated to limit short rents, as a response to their increasing unpopularity. In European cities the situation is similar, and the animosity is not addressed against US visitors but against visitors in general.
That said, there is an unquestionable rise in anti-American sentiments around the world as a reaction to the current administration policies in the US, as measured by multiple polls. However, I agree that you should not expect any uncomfortable situations if you are kind, empathic, and avoid discussing politics. The way how this anti-American feeling expresses the most is not by people being unkind or violent towards US citizens visiting other countries, but rather by foreigners avoiding to travel to the US. Anyone can make a quick google search and find that the incoming tourism has significantly dropped to the US, specially from Canada and Europe.
So, Americans should not be afraid of visiting other countries; it is the people from other countries who are increasingly afraid or not interested in visiting the US.