Why don’t right-wing Russians view with him more suspicion?
Putin has been skillful managing the Russian nationalist feelings. I don't claim to be an expert in Russia, but I am certain that raising this question on purely ideological grounds is a wrong approach. You should better pay attention to sentimental elements involving Russian national pride and a long tradition of autocratic rulers, from Tsar Ivan the Terrible to Joseph Stalin (also known as Uncle Joe or the Father of All Russias). Vladimir Putin can be seen as another link in this chain of strong Russian leaders. My impression is that he has managed to synthesize an amalgamation of Russian nationalism that can be consumed either by a nostalgic for the communist era or by an unrepentant tsarist, not based on theoretical or ideological grounds but on sentimentalism.
