[Context: The Russian proposal of a common “House of Europe” from Vladivostok to Lisbon]
The new-old enemy image of Russia serves the West above all to distract from its own social and democratic dismantling.
While aware of pro-Kremlin disinformation campaigns, the West is trying to keep open channels of communications and cooperation with Russia. For instance, NATO as the Western organisation created cooperation bodies – the Permanent Joint Council and the NATO-Russia Council – to embody its relationship with Russia. It also invited Russia to cooperate on missile defence. The Warsaw Summit Communique 2016 describes NATO's official policy towards Russia: "The Alliance does not seek confrontation and poses no threat to Russia. But we cannot, and will not, compromise on the principles on which our Alliance and security in Europe and North America rest."
The EU and its member states have maintained a clear policy of reaching out to Russian society and youth, mainly through the Erasmus+ student exchange programme and other people to people contacts, in line with five guiding principles of relations with Russia.
For background, see EUvsDisinfo analysis "The “Russophobia” Myth: Appealing to the Lowest Feelings" here.