Better Robes + Anonytroll's updated patch for Tamriel Rebuilt work great for the most part.
There is a small issue where a common robe is missing part of a texture. This issue only seems to affect some people. The original creator of the updated patch was not able to reproduce the issue.

This archive contains a fix for this issue, it changes one of the texture paths in tr_pb_robe_com_01.nif from textures\tr\c\tr_c_robe_com_05ufh.dds to textures\tr\c\tr_c_robe_com_05_uf.dds.
Just made this a file that can be easily downloaded instead of having to download NifSkope and do it manually.

If any of the original creators of the mod or patch want this taken down for any reason, I can.