It's neutral. How can it be anti-state? The network just continues regardless what the state does.
The state is inherently based on power over people. If Bitcoin continues regardless of what the state does it challenges the primary distinguishing feature of the state and thus it's inherently anti-state.
Bitcoin is a system that cannot be controlled by any single person. It's no more anti-state than the Sun is.
If a government loses its power it's no longer a GOVERNment, it's a company. Everything that challenges its power is thus inherently anti-government. Sun would be anti-government too if state wanted to control it but it doesnt. It does want to control money though.