TL;DR Putin is not a right-wing politician, he is tricking western right-wingers to think so to backstab them, when the time will come.
I'm tired to see, how alt-right praises Putin. The idea, that Russia is somehow conservative country and Putin is somehow "nationalist" politician, has nothing to do with reality.
Real policies of Russia are anti-europeanism, anti-westernism, anti-fascism, pro-sovietism, pro-corruption.
Just show me any speech/publication by any russian politician, who is not in jail, which would be pro-european, pro-white, anti-communist.
Show me ANY factual evidence, that Putin is anti-communist or nationalist.
On the other hand, there are plenty of evidence of the opposite:
Putin says, that he is still into communist ideas
cnsnews.com
Russian Patriarch awards a medal to the leader of the Communist Party of Russia
rferl.org
Putin is concerned about rise of "neo-nazism" in Europe
themoscowtimes.com
Russian Foreign Minister condemns "glorification of Nazism" by the US and Trump's anti-muslim policies
tass.com
Russia condemns rename of Moscow's avenue by the name of Ukrainian nationalist in Ukraine
tass.com
Russia is concerned about rehabilitation of Nazism in Europe
tass.com
Russia is concerned about raising Nazism in Ukraine
tass.com
"Fighting against Neo-Nazism one of Russia’s foreign policy priorities"
tass.com
Russia is concerned about revival of Nazism in Europe
tass.com
"Attempts to falsify (OP - to step out of anti-fascist allied propaganda) history of WWII undermine foundations of modern world order"
tass.com
Putin calls for fighting any manifestations of Nazism
tass.com
And this is only what I've got from 15-minute random browsing. Just show me somthing comparable, that would prove, that Putin is secretly a conservative?
In the early time of USSR KGB used a trick to defeat right-wing opposition - to create fake right-wing groups and then just kill everybody who would enlist:
en.wikipedia.org
And I think that there is something similar is going on here. Why else a neo-communist regime, lead by a KGB former officers, would spread a myth, that they are fascists and make western right admire them?