Tissue rejection was a medical term that referred to the incompatibility of differing body tissue when transplanted.
Mehendri Solon overcame this problem, an ability he later used when restoring Morbius. (TV: The Brain of Morbius) The same issue was faced on Thoros Beta by the surgeon Crozier, in his experiments of brain transference on order of Kiv. He had perfected a serum to avoid the reaction; he claimed to be able to "put any brain in any body anywhere". (TV: Mindwarp)
Cyber-conversion only worked on Mondasians and humans. The genome of other species made the process falter, resulting in tissue rejection. (COMIC: The Flood) however the Cybermen overcame the problem and were able to convert all organic life, even Time Lords, into Cybermen. (TV: Nightmare in Silver)