A Study of Tacrolimus/Methotrexate/Ruxolitinib Versus Post-Transplant Cyclophosphamide/Tacrolimus/Mycophenolate Mofetil in Non-Myeloablative/Reduced Intensity Conditioning Allogeneic Peripheral Blood Stem Cell Transplantation (BMT CTN 2203)

Inclusion Criteria: * Age 18.0 years or older at the time of enrollment. * Participants undergoing allogeneic HCT for one of the following indications: * Acute leukemia or chronic myelogenous leukemia with no circulating blasts and with less than 5% blasts in the bone marrow. Therapy related myeloid neoplasms are allowed. * Myelodysplasia/chronic myelomonocytic leukemia with no circulating blasts and with less than 10% blasts in the bone marrow (higher blast percentage allowed in MDS due to lack of differences in outcomes with \< 5% versus 5-10% blasts in this disease). Therapy related myeloid neoplasms are allowed. * Lymphoma \[follicular lymphoma, Hodgkin lymphoma, diffuse large B cell lymphoma, mantle cell lymphoma, peripheral T-cell lymphoma, angioimmunoblastic T-cell lymphoma and anaplastic large cell lymphoma\]. * Planned NMA/reduced intensity conditioning regimen. * Participants must have a related or unrelated PBSC donor as follows: * Sibling donor must be a 6/6 match for HLA-A and -B at intermediate (or higher) resolution, and -DRB1 at high resolution using DNA-based typing and must be willing to donate peripheral blood stem cells and meet institutional criteria for donation. HLA-matched parents and children may be used as donors. * Unrelated donor must be a 7/8 or 8/8 match at HLA-A, -B, -C and -DRB1 at high resolution using DNA-based typing. Unrelated donor must be willing to donate peripheral blood stem cells and meet NMDP criteria for donation. * D…