i don't have a good answer for this, but i think it deserves conversation, so i'm jumping in anyway.
loyalty to me is what people do in the face of enmity. ie, i am critical of my friends when it's just us, and not critical (mostly) of friends when we are around or fighting with people-not-my-friends. that decision not to be critical in certain contexts is what i call loyalty, as well as the decision to stay in relationship even when i disagree with someone's decision(s).
(the level of relationship and the level of disagreement is meaningful, of course.)
this conversation is complicated for me by my rejection of a kind of secrecy that i associate with drug addiction and family dysfunction (which i guess ties back to my initial paragraph by challenging who gets defined as an enemy, which can be confusing).
so loyalty is important when emotions and theory are in synch? and it's not loyalty but codependency (ew!) when it stunts us more than it teaches us?
well, maybe a start, anyway.