Comparing ATG or Post-Transplant Cyclophosphamide to Calcineurin Inhibitor-Methotrexate as GVHD Prophylaxis After Myeloablative Unrelated Donor Peripheral Blood Stem Cell Transplantation

Inclusion Criteria: * The following diseases will be permitted, although other diagnoses can be considered if approved by Fred Hutch Patient Care Conference or the participating institution's patient review committees and the principal investigator: * Acute lymphocytic leukemia (ALL) in complete remission (CR)1 with high risk features defined as evidence of adverse cytogenetics such as t(9;22), t(1;19), t(4;11), or MLL rearrangements or presence of minimal residual disease * Acute myeloid leukemia (AML) in CR1 with high risk features defined as: * Intermediate or adverse risk disease as defined by European LeukemiaNet (ELN) 2017 * Greater than 1 cycle of induction therapy required to achieve remission * Preceding myelodysplastic syndrome (MDS) or myelofibrosis * Therapy-related AML * Presence of FLT3 internal tandem duplications * French-American-British (FAB) M6 or M7 classification * Acute leukemia (ALL or AML) in second (2nd) or greater CR (CR ≥ 2) * Refractory or relapsed AML with =\< 5% bone marrow blasts and no circulating blasts by morphology or proven extramedullary disease * Myelodysplastic syndrome (MDS) with following high risk features: poor cytogenetics (-7, inv(3)/t(3q)/del(3q), del(7q) or complex cytogenetics defined as \>= 3 abnormalities), Revised International Prognostic Scoring System (IPSS-R) risk group intermediate or higher, or treatment-related MDS * Any phase of MDS if patient is \< 21 years of age * Chronic mye…