Never Trump and Putin do not get along with each other. America's interests do not coincide with the interests of Russia. How tiger can get along with the kid? It is not possible. Russia is an enemy of America.
If Russia and the U.S. both have the goal of remaining sovereign and independent nations (or re-achieving that mode as the case may be) then they do have interests which coincide. If there are 'Davos Man' type people and groups who seek to integrate the two nations...or get them to mutually destroy one another for strategic reasons...then the two nations might recognize a common enemy.
As far as I can see, most of the rivalry between Russia and the United States is caused as a result of inflammatory rhetoric from the politicians from both sides. I am not just referring to the American politicians such as John McCain and Hillary Clinton, but also to the Russian extremists, such as Vladimir Zhirinovsky and Alexander Belov.
I don't know about the Russians, but it is crystal clear that Clinton received massive support from the 'Davos Man' types that I alluded to. Thankfully it was not enough. McCain, along with Ryan, are also recently rumored to have been a beneficiary of support originating from Soros-land. That would explain a lot. Notably both Clinton and McCain are finally permanently and irreparably damaged here in the U.S., but it sure took a while!
If the disruptive Russian politicians you mention are similarly corrupted, hopefully they'll be identified and run out on a rail as well. Especially if the growth of citizen-driven information gathering and analytical thesis can persist. That will be an area of conflict going forward I think, and I think there is a fair chance that 'we' will win this struggle. Or at least have enough 'surges' to stay in the fight.