Here is a patch to add support for more types on btree_gin.
I was missing UUID type, so I added it. Since I was there, I checked all other built-in types with B-tree but not GIN support, and the remaining list was: uuid, bool, name, bpchar and anyrange (at least ones that seem to make sense to me). So I added support for all of them.
If you have any other type I missed and you wish to have support to, please let me know and I can add it.