Is this a DBWI? The US did give aid to Tito to keep him afloat after his break with Stalin.
http://www.psupress.org/books/titles/0-271-01629-9.html In the 1970's it tilted toward China against Russia--it even supported Pol Pot retaining the UN seat for Cambodia aftee the Vietnamese invasion of that country...
Yeah, especially post-Vietnam, US foreign-policy was not as anti-Communist as both its defenders and opponents made it out to be. Granted, at least with China, there was probably the idea that people like Zhou Enlai and Deng Xiapoing(ie. the faction the US was reaching out to, even while Mao was still alive) were the more pro-capitalist group in the CPC.
That said, assuming that "anti-Soviet" means "anti-Russian", the biggest differences between OTL and the OP's scenario might be in the rhetoric employed by US government propaganda. Less emphasis on the evils of Communism, more on the supposed barbarism and savagery of Russians(and whichever Slavic groups were allied with them). I guess comparable to the way the gutter press portrays arabs and Mulims today.
Also, the Cold Warriors in the US would probably be way more suspicious of people like Solzhenitsyn, and Russian nationalists generally. They might cynically latch onto a few stats and anecdotes from The Gulag Archipelago for propaganda purposes("See, look how horribly those subhuman Russians treat each other!!"), but you wouldn't see that book's author lionized on the cover of National Review, as you did in real life.