1. We have an unusually high tolerance for bureaucracy. Forms, notaries, arbitrary office hours, waiting rooms and sign-in sheets, stamps and control numbers -- we've seen it all, and have been living it for a career. After a few years, you just eventually grow numb to it all. Building a dossier isn't really that big of a deal. The process of clearing most CONUS installations prior to PCS is just as hard, if not more so.
2. We are used to having our personal fate decided by arbitrary and distant administrators. Promotions, assignments (moves), and school opportunities are routinely decided by anonymous boards or administrators far away, based on policies and requirements that are frequently shrouded in secret. Every three years or so, your family gets pulled to some new location -- all faithful servants of a personnel system designed during WWII. So, the whole notions of arcane dossier acceptance policies, nationally centralized adoption authorities, and esoteric quota systems all seem perfectly natural to us.
3. Unmatched system of social welfare. If you think your only qualification to be a parent is that you once (barely) completed Basic Training, have no fear. The vast array of DoD-sponsored social services that are part of you well-earned compensation. Here is a look at some of the offerings at our small local garrisons. Don't forget health care, legal services, after-school programs, recreational programs, youth sports, family-friendly dining facilities, regulated child care, and much more.
On a bit more serious note, I think military families might also tend to be more open to international or trans-racial adoptions, as well. Many of us have traveled or lived abroad extensively, and that will definitely change your perspectives on different peoples and cultures. From my personal experience, I will say with certainty that my own travel has dramatically increased my sympathies and sensitivities towards other cultures.