Pre-transplant Immunosuppression and Donor Stem Cell Transplant for the Treatment of Severe Hemoglobinopathies

Inclusion Criteria: * Patients 2-30 years-of-age with confirmed sickle cell disease (SCD) (SS \& sickle beta \[SB\]-thalassemia, both sickle beta 0 \[SB0\] and sickle beta plus \[SB+\]) or severe B-thalassemia major are potentially eligible * Patients with SCD should also meet the following eligibility criteria as outlined by the Center for Medicaid and Medicare Services: sickle cell disease and at least one of the following: * Stroke or neurological deficit lasting \> 24 hours * Recurrent acute chest syndrome (ACS): 2 or more episodes of ACS in 2-year period preceding enrollment * Recurrent vaso-occlusive pain crises: 3 or more episodes per year in 2-year period preceding enrollment or recurrent priapism (3 or more episodes in the 2 years preceding enrollment) * Chronic transfusion program defined as 8 or more packed red blood cells (PRBC) transfusions per year to prevent central nervous system and/or vaso-occlusive complications in 1-year period preceding enrollment * Impaired neuropsychological function and abnormal cerebral magnetic resonance imaging (MRI) scan (silent strokes) * Stage I or II sickle lung disease * Sickle nephropathy (moderate or severe proteinuria or a glomerular filtration rate 30-50% of predicted normal value) * Bilateral proliferative retinopathy and major visual impairment in at least one eye * Osteonecrosis of multiple joints * Echocardiographic finding of tricuspid valve regurgitant jet velocity (TRJV) \>= 2.7 m/sec * Patients with B-thalassemia are considered as severe if they are/have any of the following: * Transfusion-dependent * Evidence of extra-medullary hematopoiesis * Pesaro Class III * Patients shall not proceed to HCT without confirmation of primary diagnosis by review of available newborn screening results or hemoglobin electrophoresis and/or genetic testing * DONOR: High resolution HLA typing will be performed on all willing and available biologic parents and siblings without clinically significant hemoglobinopathy. Preference will be given to donors with the lowest number of HLA-allele mismatches * DONOR: Donor-specific anti-HLA antibodies will be obtained and analyzed from all patients. Preference will be given to donors with absent or low titer anti HLA-donor specific antibody levels when possible Exclusion Criteria: * Uncontrolled infection * Females who are pregnant and/or unwilling to cease breastfeeding * Seropositivity for human immunodeficiency virus (HIV) * Lansky or Karnofsky performance status \< 70% * Life expectancy severely limited by concomitant illness * Uncontrolled arrhythmias or symptomatic cardiac disease * Uncontrolled symptomatic pulmonary disease * Evidence of chronic active hepatitis or cirrhosis * Serum conjugated (direct) bilirubin \> 2 x upper limit of normal for age. Participants are not excluded if the serum conjugated (direct) bilirubin is \> 2 x the upper limit of normal for age as per local laboratory and: * There is evidence of a hyperhemolytic reaction after a recent red blood cell (RBC) transfusion, OR * There is evidence of moderate direct hyperbilirubinemia defined as direct serum bilirubin \< 5 times upper limit of normal (ULN) and not caused by underlying hepatic disease * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) \> 5 x upper limit of normal for age * Serum creatinine \> 1.5 x upper limit of normal for age AND estimated or measure creatinine clearance \< 70 mL/min/1.72 m\^2 * Patient, parent or guardian unable/unwilling to provide consent and when indicated, assent * Patients with available HLA-matched related donor * Prior receipt of gene therapy * DONOR: All potential donors shall be tested by hemoglobin electrophoresis. Any potential donor with a clinically significant hemoglobinopathy will be deemed ineligible. Donors with sickle cell trait and beta thalassemia trait are eligible to donate