Brazil already conducts enhanced scrutiny of Americans..

" American citizens are both photographed and fingerprinted as part of their immigration clearance process. This is because Brazil practices diplomatic reciprocity and processes American citizens entering Brazil the same way the U.S. processes Brazilian citizens entering the United States. This is most assuredly NOT the place to demonstrate any displeasure with this process. More that a few Americans (including at least one airline pilot) have been arrested, fined (thousands of dollars) and ejected from the country forever for making an obscene gesture during this process."

http://www.brazil-help.com/brazil_travel_tips.htm

http://www.economist.com/blogs/gulliver/2013/02/tourist-visa...

Note that this predates the Trump administration.

If people want to self-identify as rude and unable to understand the difference between creators and implementers of policy, I vote we let them.

I'd rather they were turned back at the border. It would be great if we could apply this to people currently in the nation as well.

I think that's the only real power that other countries can exercise - force Americans (especially business travelers) to experience what the US is forcing on visitors in the US.