LONDON—Every four years, U.S. expats hear the same story: that this U.S. presidential election will be a tight one, and that it is crucial for registered voters to get out and vote—and for those who are not registered, to do so soon, because every vote counts.

The choice between Hillary Clinton and Donald Trump may be one of the most intense in recent memory, with supporters on both sides of the aisle passionate for their candidate with an equally burning hot hatred for their rival. For the more than three million Americans...