We are not talking about libertarian idealistic theory here, but the current situation.
Just as free movement across borders becomes problematic in a welfare state, so the current existence of nation-states with their frequent conflicts and opposing interests throws a monkey wrench in the issue of dual or multiple citizenship.
If a Ron Paul clone were presiding over each nation, and their deliberative bodies supported libertarian principles, then there would be no problem.
Today however, when we have another country telling this one "Lets you and them fight". then we have a problem when the US official is a citizen of that other country.
You want to a dual citizen of Uruguay? Have at it.
You want to be a dual citizen of, say, the Peoples Republic of China and be US Secretary of the Treasury, that becomes a problem.