The emphasis on respect and reputation in The Things They Carried is an inevitable byproduct of the focus on friendship and weakness. The soldiers fear and loathe weakness, so in order to keep their friendships intact, they need to protect their reputations. When all the soldiers freak out in a firefight, they're able to laugh about it later. But when one gets an extremely embarrassing wound (or shoots himself in the toe to get out of the war, or freezes in a firefight, or doesn't partake in a particularly morbid joke, and so on), the soldier bristles to protect his reputation.
Because the soldiers rely on friendships with other soldiers in order to stay sane, and because they have a terror of weakness, reputation becomes incredibly important. If they appear weak and lose their reputations, they fear they may lose the friendships they need to survive.
While the soldiers believe that toughness in battle and a willingness to kill is what earns them respect, in fact, it's not the case. Decency and moral character earn far more respect with the soldiers than indifferent toughness does.