I labelled the above idea space “liberalism” but I’m not convinced it’s the right term. I am just lacking a better one. In any case, if we assume the to be the status quo, which I think we mostly can, people trying to preserve these values and bolster them are conservative. They enjoy the status quo, wish to keep it and wish to reinforce it. They wish to prevent progress ( as in movement ) towards a different direction.
There is also another idea space, generally associated with christian identity, belief in God, the existence of two biological sexes with clear roles to fulfil, european heritage, abortion is murder, sex strictly within marriage, no homosexuality, gun rights, etc
This would be called conservatism. But, as in the “liberalism” mentioned above, it’s not really the best term. If we just take it as an idea space and assume liberalism to be the status quo, this would definitely be a counter culture.
It dislikes the current status quo, wishes to undermine it and shift it in a different direction.
And, in this sense, I agree with the person you responded too. “Conservative” is the new counter culture.