Allogeneic hematopoietic stem cell transplantation (HSCT) represents the only viable cure for children who suffer from a wide variety of rare, serious non-malignant diseases, such as Fanconi Anemia, Hurler syndrome, and hemophagocytic lymphohistiocytosis. A major obstacle to the success of HSCT is morbidity and mortality from graft versus host disease (GVHD), driven by donor T cells recognizing and reacting against disparate host antigens. This trial is being conducted as a step toward testing the long-term hypothesis that the costimulation blockade agent abatacept can be added to a standard post-transplant GVHD prophylaxis regimen, cyclosporine and mycophenolate mofetil, to improve disease-free survival after unrelated hematopoietic stem cell transplantation (HSCT) using reduced intensity conditioning for children with non-malignant diseases (NMD). This study will have the following Specific Aims: