Yes, there does need to be an intention to relinquish US nationality in order for US nationality to be lost. It doesn't have to be explicitly stated, but it doe

Yes, there does need to be an intention to relinquish US nationality in order for US nationality to be lost. It doesn't have to be explicitly stated, but it does have to be there. If it ever needs to be disputed in court, whoever is arguing loss of citizenship (either the government or the would-be former citizen) has to prove that intent by the same standard of proof that's generally required to win a civil lawsuit, preponderance of the evidence aka more likely than not. I agree it's not clear that accepting the papacy involves intent to relinquish, but it's not clear either way. The Department of State (at first instance) or any court who considers the matter (if a dispute arises) would normally consider the individual situation in order to conclude what they think is the intent. In practice, if Trump and Rubio don't want an international incident, they will probably just ask the Vatican what the Pope intended and go along with that.