That said, it doesn't do a lick of good to have an ICE contact set up if, when the first responder picks up your phone, it asks for a password to get into it. It's one of those cases where you need to weigh the balance on convenience vs security.
Have the ability to configure this stuff on the lock screen.
Either text (this phone owned by bleh) or a maybe a button to dial an emergency number.
Have it just display something like "Emergency contact" who you can dial without displaying any more information on the person, not even the phone number when it dials.
Having this person know personal information about you (blood type, etc) would then still be relatively secure versus openly available, and the person would have little risk of getting prank called if your phone is stolen outside of an emergency situation.