I don't know how race (appearance) has anything to do with attachments?
There are like hundreds to thousands of Jedi from time to time. I'm sure that someone else can appointed to settle dispute involving someones home planet if they reason (rational mind) that they can't stay impartial. One can also reason that even maybe saving live is more important than beloved ship.
"Saving only one" is a very precise problem, but if you can save only one (no other outcome, no way) who rational beign would save someone you know nothing about instead of person you know and care for? Should I save someone unknown just because the other one is "forbidden" attachment, makes no sense.
It all comes (again) down to the fact that you must judge every situation as they come and use reason to temper emotions.
As I said. I see Jedi Code as a guideline for the young and immature. I could never be so cold that is expected of the Jedi. The code is made to fail. Not now, not for everyone and not everytime, but with living beigns (not droids) the failure is always there.
Save the Supreme Chancellor or your partner and fellow jedi. Well that would be a puzzle
Also very unlikely situation.