Does anarchy mean “anything goes”, assuming that the NAP is not violated?
Yes and no.
Yes, because you would be free to do as you wished so long as you didn’t violate the NAP.
No, because others’ equal freedom to do as they wish means that they could do anything OTHER than violating the NAP to affect your behavior.
The example of IP laws
To take an example commonly discussed. there could be no IP (“intellectual property”) laws in an anarchy, because such laws require a State to enforce them.
But let’s suppose that everyone, or almost everyone, in that particular anarchy believed that creators of IP deserved payment for their work, and thus that copying such work without their permission would be an inappropriate act, deserving social disapprobation.
In such a situation, those who did copy would find themselves isolated from the rest of the community. Violence could not be used against them without violating the NAP, so they would be free to continue this behavior if they wished to do so. However, they would probably find it too expensive to continue, in terms of lost opportunities for interaction with others.
Conclusion
If the vast majority of members of society disapprove of a particular behavior, such behavior would be deterred even in the absence of violent prevention of that behavior, especially in a business setting; no businessman wants to face boycotts that seriously impact his ability to sell.