Is there a reliable way to determine if a chemical system is more suited to be calculated using a multireference method instead of DFT?
You should have a look at the so called FOD (Fermi Occupied Density) analysis by Grimme et al. That is accessible by ORCA 4 very easy and straight forward by specifying "FOD" as a keyword. [1-3]


From ORCA Input Library [1]:


  The FOD plot above (plotted with Chemcraft) indicates a significant and delocalized FOD. Multiconfigurational methods should be used to study this molecule and any single-reference result (HF, DFT, MP2, CC should be regarded with suspicion)




Via Multiwfn you can access the "local total/dynamic/nondynamic electron correlation function" and "total/dynamic/nondynamic electron correlation index" [4,5].


Visual abstract from [5]. You can see the dynamic and non-dynamic correlation from which you also can see if single reference methods are acceptable or not.



[1] ORCA Input Library, FOD analysis
[2] S. Grimme, A. Hansen, Angew. Chem. Int. Ed. 2015, 54 (42), 12308-12313
[3] C. A. Bauer, A. Hansen, S. Grimme, Chem. Eur. J. 2017, 23 (25), 6150-6164
[4] E. Ramos-Cordoba, P. Salvadorc, E. Matito, Phys. Chem. Chem. Phys. 2016, 18, 24015-24023
[5] E. Ramos-Cordoba, E. Matito, J. Chem. Theory Comput. 2017, 13 (6), 2705–2711