The Constitution doesn't mention geography, that's true. That could either be because the framers intended it to apply to everyone everywhere, or because they thought it was obvious it would only apply to Americans in America.
Luckily, the Constitution is not a disembodied bit of text. We have copious context to use to evaluate the significance of the lack of geographical distinctions in the Constitution. The English legal tradition, which the Constitution is a product of, is highly territorial. English law applied to Englishmen in England. Thus, it is reasonable to conclude that American law, including the Constitution, was intended to apply to Americans in America.
Scalia's dissent in Boumediene has a good discussion of the application of Constitutional rights to non-citizens: http://www.law.cornell.edu/supct/html/06-1195.ZD1.html. I'd skip to Section II to get past the political rant.
It is obviously more nuanced than you make it seem. Do you really think it would be constitutional for the government to target a specific religion or race with drone strikes as soon as any of the targeted group were to go on vacation in e.g. the Bahamas? I don't necessarily disagree with your conclusion with regard to the current drone strikes, but I think your rational/analysis is deeply flawed and there certainly isn't a complete trashing of the constitution as soon as a citizen leaves our borders.
I'm not clear on how "No person..." selects some subset of people with whom such government prohibitions apply.
You're looking at it wrong. It's that the text does not allow for a certain class to be excluded, which is what the Obama Administration is doing with respect to "military-age males."
I'm not clear on how "No person..." selects some subset of people with whom such government prohibitions apply.
>at the time of the founding it was taken for granted that the Constitution only applied to American soil.
The Constitution makes no mention of geography. Instead it is entirely a collection of MAYs, SHALLs, and SHALL NOTs directed at the government.
>Most of the extra-territorial application of the Constitution...
...is predicated on notions of geographical distinction wholly absent from the Constitution.