For one thing libs hate Russia so naturally conservatives whose positions are largely determined by whatever will “trigger” the people on the other side the most will tend to be more sympathetic toward Russia.

Also, the social conservatism of present day Russia appeals to them, they feel like Russia is on their side of the culture war, and in some cases this is true like on LGBT issues, but in others like abortion for instance this is very much not the case…of course they probably don’t know this because they never actually bothered to learn what Russia is really like, instead forming a caricature of it in their heads as this haven of “traditional” values and Christianity, much like libs have a caricature understanding of Russia as a dystopian dictatorship.

It also helps that the Russians themselves (including i believe Putin himself? …but someone can correct me on this if i am wrong) use some of the language that American conservatives like to use, terms like “globalist” and so on (except the Russians are mostly using it to mean “imperialist” whereas American reactionaries think it refers to their conspiracy theory of this cabal plotting to establish a New World Order and eat babies for breakfast or whatever other shit the right wing comes up with).

There is some ideological overlap but a lot is also imagined. Mostly it’s contrarianism as you say. Plus they are easily swayed by aesthetics and the notion of Putin as a strongman as he is commonly in western mainstream media appeals to them. And they view Russia as a white Christian nation (again a misconception on their part, Russia is very diverse) so they don’t have the racism toward it that they do against Iran or China.