Hexbear isn't simply anti-west, but anti-imperialism. As in, Lenin's definition. As extreme shorthand, Lenin defines Imperialism as the point at which Capital has concentrated to the point of near monopoly so as to impact the state's decisions, a merging of bank and industrial Capital, export of Capital (not commodities), formation of international monopolies, and territorial division amongst the greatest Capitalist monopolies.

Following this, Russia does not hold the same extreme economic power internationally that NATO countries do, so while hexbear condemns Putin as a bourgeois dictatoraship and seeks an immediate end to the conflict, they also believe NATO as an imperialist power cornered Russia into making a move, provoking it.

Hexbear is usually anti-west because the West absolutely fits Lenin's definitions.

That's pretty much it, if you are familiar with Lenin and agree that opposing the strongest Capitalist powers is a good thing, you'll agree with some part of hexbear.

It's also worth noting that hexbear isn't simply Putin supporting, they would rather the Communist party rule Russia, but if they have to pick sides, they would rather support the anti-Imperialist side (again, Lenin's definitions) than the Imperialist side (yet again, Lenin's definitions).

That's really all there is to it.