Hi,
It's difficult to give an exhaustive list since there are quite a few methods implemented in Turbomole nowadays. Definitely "basic" HF/DFT/TD-DFT handle non-abelian point groups very well (dscf/grad/ridft/rdgrad/escf/egrad). Of course there are always some exceptions...Since you are interested in MP2 optimizations, the ricc2 module does support non-abelian point groups at least for ground-state MP2 (at least the serial and OpenMP parallel versions, the MPI parallel version did not support them the last time I checked).
Best,
Antti