Risk of rejection is very minimal with HUMAN mesenchymal stem cells (MSC) because MSC are discovered to be hypoimmunogenic.* This means that these MSC have a resistance to the normal immune response and as such do not pose much of a risk for hypersensitivity reactions. Many case studies have suggested that transplantation of MSC could be beneficial in patients with various disorders requiring tissue regeneration, and provide evidence supporting the tolerance of allogeneic MSC by recipients.  Mesenchymal stem cells are a highly regulated self-renewing population of cells with potent mechanisms to avoid allogeneic rejection.
*ReferenceJennifer M Ryan et al, Mesenchymal stem cells avoid allogeneic rejection J Inflamm (Lond)v.2; 2005PMC1215510