There is a line between exhibitionism and naturism, which can be defined as the intent. Exhibitionists have the intention to display their privates, to grab attention to their sexual body parts for sexual pleasure. Non exhibitionist naturists happen to be naked, with their privates in full view without the intent of grabbing attention to those sexual body parts. Of course, there’s always a possible misinterpretation of intention, but this is the exception not the rule. So to answer the question in the title, we can say nudists’ private are public. However, this does not make them the center of the attention. This is why “true” nudists look at each others in the eyes, IMHO.