...now that the UK is packing up and politically retreating back across the Channel, the admiration Americans hold for Britain will also falter as the openness and tolerance of our British cousins will increasingly be called into question.This is an ill-phrased and possibly ill-timed remark, it seems to me. I would have voted Remain, but I don't think "packing up" and "retreating" really capture what's going on here -- at best, it's a partial description.
Moreover, I don't see sentiment about Britain in the U.S. being affected that much. Americans who were anglophiles before Brexit will still be anglophiles. British history and 'high' culture, e.g. literature (by which I mean to include the history/culture of the UK's constituent parts), are, to a large extent, what American anglophiles admire, and I wouldn't anticipate that feeling changing drastically, if at all.