This phase II trial investigates how well a naive T cell depleted graft work for the reduction of graft versus host disease in patients with non-malignant diseases requiring hematopoietic cell transplantation. Giving chemotherapy and total-body irradiation before a donor peripheral blood stem cell transplant helps stop the growth of cells in the bone marrow, including normal blood-forming cells (stem cells) and cancer cells. It may also stop the patient's immune system from rejecting the donor's stem cells. When the healthy stem cells from a donor are infused into the patient, they may help the patient's bone marrow make stem cells, red blood cells, white blood cells, and platelets. The donated stem cells may also replace the patient's immune cells and help destroy any remaining cancer cells.

OUTLINE: Patients will receive CD34+ enriched CD45RA-depleted donor T-lymphocytes IV on day 0. For conditioning, patients receive cyclophosphamide by IV on day -8, fludarabine by IV on day -7 to day -3, thiotepa IV on day -7 and day -6, and undergo total-body irradiation (TBI) for 2 doses on day -2 and day -1.

GVHD Prophylaxis:

All patients also receive tacrolimus IV continuously starting on day -1, and mycophenolate mofetil (MMF) starting day 0 through day 35. If there is no evidence of grade II-IV acute GVHD on or prior to day 100, tacrolimus is tapered.

All patients also undergo bone marrow aspiration/biopsy and collection of blood samples throughout the trial.

After completion of study treatment, patients are followed up at days 7, 14, 21, 28, 56, 80, 180, and 270 and at 1, 1.5, and 2 years.

Inclusion Criteria:

• Considered appropriate candidate for allogeneic HCT following low dose (4Gy) TBI containing-conditioning and have one of the following diagnoses: A) BMF B)Hemoglobinopathies C)PID D) Autoimmune cytopenias E) Immune dysregulation F) HLH G) Other NMD treatable by HCT and NMD that is not clearly defined (a patient with a NMD for whom genetic testing has been done and a genetic mutation responsible for their NMD phenotype has not been identified) are eligible for the study following discussion with and approval by the protocol PI
• Patients aged 6 months- 5 years old (inclusive) at the time of informed consent
• Patient with suitable HCT donor (see inclusion criteria below)
• Recipient informed consent/assent (13 years and older), and/or legal guardian permission must be obtained

Exclusion Criteria:

• Patient with aplastic anemia
• Patients with severe combined immunodeficiency (SCID)
• Fanconi anemia
• Dyskeratosis congenita
• Patient weight > 100 kg
• Patients who are positive for HIV-1, HIV-2
• Patients with current neoplastic disorders
• Patients with uncontrolled infections for whom HCT is considered contraindicated by the consulting infectious disease physician.
• Patients with organ dysfunction including A) Renal insufficiency B) Impaired cardiac function C)Impaired pulmonary function D) Liver dysfunction
• Patients who are pregnant or breast-feeding
• Patients on other experimental protocols for prevention of GVHD
• Patients of childbearing age who are presumed to be fertile and are unwilling to use an effective birth control method or refrain from sexual intercourse during and for 12 months post-HCT
• Patients with any other significant medical conditions that would make them unsuitable for transplantation, as determined by the PI
• Patients with a known hypersensitivity to tacrolimus or MMF