You may not believe this, but most Russians identify as both A) European and B) Christian. Their awkward current position in the Western system is mostly just a function of their size and their unwillingness to subordinate themselves. If you read actual Russian nationalists, they have deep skepticism about BRICS and the like. Dugin is the outlier among them.
Putin's attitudes on this is shaped by his cosmopolitan Soviet past where the communists would take up every 3rd world struggle in order to stick it to the West. Most young Russians don't give a hoot what's happening in the global south nor do they identify themselves as part of it.
There's a lot of bad blood right now between the West and Russia and public attitudes reflect that fact. However, if the hostilities die down and there's some rapproachment (big ifs) then I don't see how Russia will stay in the "third worldist" camp for long.