Kind of a random topic, but there are often laws banning public nudity. Presumably even nudity that can be seen in public, but which takes place on private property (say someone is showering or sunbathing in the nude outside).
How would this issue be dealt with in ancapistan or under a "free" government?
It depends on what kind of place you live in. A controlled community with deed restrictions, apartment building, or truly "free" land, most likely in a rural area. Obviously if you're renting then the property owner can kick you out for being a nuisance so I assume you're not asking about that. Most people would live in some hybrid zone where you technically own your land, or are part owner, but you have deed restrictions or the dreaded HOA setting community rules, so things wouldn't be that much different than today. Disputes would go to an arbiter. Communities of nudists could make their own rules.
Otherwise generally anything goes on your own property, but if you are being a nuisance to neighbors (which could include anything audible or visible to them) they might take you to court. A judge would decide if either party can do something to mitigate the problem, like put up a higher privacy fence. Depending on the court if an agreement isn't reached they might rule it a NAP violation.
Even now plenty of rural areas have no laws on public nudity, so again it wouldn't be all that different.
case by case. in his/her own yard - maybe - as long as they aren't wacking off in the front yard. But, nudity doesn't equal sexual acts.
If they are morbidly obese or are as hairy as a gorilla, no! my eyesight is dear to me. Nude beaches and parks - yes. sitting nude on a park bench without a towel underneath them - no - unsanitary.
Is it a violation of NAP?
Yes => it is not allowed
No => then it depends on the property owner
Most property owners are influenced by what their customers want. If most people are grossed out by nudity then most places will ban it. But as long as there are some nudists around then the incentive will exist to establish nudist friendly places to capture their market share. So everybody wins.