Counter culture by definition counters some established cultural paradigm. It is at least critical, and at most actively hostile - but cannot by its very nature be apolitical, much less maximally accepting.
Counterculture among the right would be the alt-right/white supremacist movements and QAnon, which counter mainstream conservatism. Among the left it would be actual (not the American definition of "anyone to the left of Reagan") communists, tankies, black and indigenous activism, etc.
It's true that not every counterculture has to be defined, or define themselves, along the left/right axis, but given the greedy nature of that axis, it seems inevitable that any counterculture could be.
Counterculture among the right would be the alt-right/white supremacist movements and QAnon, which counter mainstream conservatism. Among the left it would be actual (not the American definition of "anyone to the left of Reagan") communists, tankies, black and indigenous activism, etc.
It's true that not every counterculture has to be defined, or define themselves, along the left/right axis, but given the greedy nature of that axis, it seems inevitable that any counterculture could be.