Rabbi Dov Linzer, head of Yeshivat Chovevei Torah in Riverdale, addressed this briefly in this video. He says that these issues are more minhag and appropriateness questions than strict halachic ones. He adds that the issue is currently being discussed by the New York Board of Rabbis, but he offers a suggestion as follows: for a transgender woman that has male genitalia, women should do taharah while the genitalia are covered. Then men should deal with the genitalia, since it would be uncomfortable for women to deal with male genitalia, and then leave the rest to women. This affirms the person's gender identity while leaving genitalia issues separate. For the case of a post-op transgender woman, the implication seems to be that women may do the full taharah.
I would an additional comment that according to Shulchan Aruch Yoreh Deah 352:3, we are more lenient on women taking care of men than the reverse, but I've heard that this is not generally done in practice.