One of the two is a US citizen, and usually nation states are bound to protect the rights of their citizens abroad.
I'm a German and I'd say, yes the German state is supposed to help such a person.
In fact, every state that signed the Vienna Convention on Consular Relations is bound by law to do so, per Art. 5 lit a of said Convention.
You're going to have to explain what you mean a bit more. I'm not getting the relevance at all.
In other words, US citizens travelling the world would prefer to know before they get into trouble overseas which behaviors their State Department considers so egregious as to disqualify them for the help that citizens can usually expect. Ergo, the State Department probably publishes a list of such behaviors or situations. I am asking you whether if it were your job to specify such a list, would having felony charges pending in a "US-based" (i.e., state or federal) court be on the list?
But let's suppose I want no government to have jurisdiction over me. I'm not quite renouncing my US citizenship, but I am explicitly trying to remove myself from all government control. If while doing this I run afoul of a foreign government, should I expect the US to protect me? (They may still do so, for their own sake rather than for mine, but it seems to me that I have no right to expect them to do so.)
Here's a slightly stronger version of the same issue. Ronnie Biggs was an Englishman, wanted in England and living openly in Brazil because it had no extradition treaty with England. If, while doing so, he got in trouble with Brazil, would anyone expect England to try to protect him as an English citizen? He still was one, but...
I don't want my tax money being wasted on that. Defend US interests, sure, but this isn't a US interest.