This post seems pretty vague. It might help if you defined your terms more rigorously and stated your question more explicitly.
For me the first type of loyalty is the type I give in those cases where my loyalty is due to its object's properties.
I am loyal to my diet so long as it causes me to lose weight. I'm loyal to my bosses IFF they pay me.
I tender the second type of loyalty in those cases where my loyalty is due to my properties.
I am loyal to my country because I want to think of myself as patriotic. I am loyal to my sports team because I want to think of myself as a faithful fan.
I want people to express their opinions on the following questions/idea. I guess the answer will depend on your personal definition/interpretation of loyalty, but I guess that's the point, I want to see what people think about what I consider to be an important topic.
It seems like there is a spectrum of loyalty.
Maybe on the left end we have "transactional" loyalty; as in the case of, "if my spouse doesn't cheat, I will stay with them."
Maybe on the right end we have "stubborn" or "cost-independent" loyalty; as in the case of, "if a member of my military unit dies, my unit will recover the body - burning through all available resources if necessary."
In practice, does "stubborn" loyalty exist? Is it desirable? What about when it comes to beliefs? Does it allow for institutions to flourish that couldn't otherwise? Is this type of loyalty categorically unreasonable?
I guess these all seem like prisoner's dilemma questions, about "tit for tat" strategies, etc, but I want to know how people on this site think about these matters in everyday life; in personal relationships, with regards to their own beliefs, especially toward their children (if you have children).