Current German law, and the law that existed when my children were born, requires at least one parent to be a German citizen for any children to be eligible for German citizenshp. Not sure what the law would be for children born in the UK, Spain, Portugal, Japan, Italy, etc.
I would not be happy if I found out, that because of my service to my Country, that my children were not considered Natural Born Citizens.
Full disclosure, two of my five children were born abroad on US base hospitals while I was serving on active-duty. The most accurate thing we can say with respect to their qualification as "natural-born" citizens, is that it's entirely unsettled law. Since the Supreme Court has never heard a case specifically addressing this issue, there is no definitive answer.
Having said that, I think that most constitutional scholars and most professors of law would agree that the chances of a court ruling that a child born on a base hospital to US parents, one of whom was in service to his country, was not eligible to be president, is virtually ZERO.
In fact, if you ask Ruth Bader Ginsburg, she believes that her grandson who was born in Paris (a place with no US bases) is ENTIRELY eligible to be President because he has two US parents, or so she opined in the oral arguments for Tuan Anh Nguyen v. INS back in 2000 or 2001. I suspect she isn't alone, and indeed Breyer seems to echo that opinion in those very same oral arguments.
I doubt that a Robert's Court would read "natural-born" so broadly (although Kennedy is notoriously liberal in immigration cases), but I'd be shocked if they didn't unanimously agree that children born abroad while on US military bases, are indeed eligible to be President.
My dad was a career officer in the US Army. Three of his eight children were born in foreign countries, and are not Natural Born Citizens, per our best understanding of that phrase.
I've never asked him (or my three siblings) about their feelings on this, but I suspect that they've never thought a whole lot about it, one way or the other. Their sole concern (when it was at issue) was purely about their basic citizenship. They're all US citizens with full rights and privileges. They just can't be president.