Blasphemy laws, bans on even discussing homosexuality in a positive light, extremely high income inequality more or less enforced by the state.
That's not
far-right, I'm pretty sure. It could be said to be right-wing in some of its internal policy, yes, but its internal rhetoric is overall very lefty.
Just recently, some person in the government got
massive scorn in the Russian social media for saying that not all Russians need effectively free higher education in order to be successful in life.
On top of that, I get the impression (unknown as to whether it's correct or not, given the limited sources/reading I've done on the matter) that the ability of the Russian government to make its citizens competitive in markets other than energy/material exports has been lacking lately, with the result being the current economic problems due to a downturn in oil prices and no major service sector to make up for it.
That's a generic Russian problem throughout the ages, not the government's one. We really don't like to engage in a kind of social activities that are necessary to make a non-raw-product economy internationally competitive. Been that way since the formation of the Russian people.
So far as I can tell, they would be a natural ally of US Republicans in their current form.
The Republicans would be probably horrified at the idea of free healthcare being considered normal. Same with state-subsidized higher education, and largely standardized - and also mostly religion-free, last time I checked - elementary and middle school education.