The problem with the term naturist is that many people confuse it with 'naturalist' (from the word natural)
Looking at the word nature - ist, it seems confusing. So it seems to be the right suffix as the word nature comes from a Latin root (if English/Germanic root then it would be 'naturer').
The next link shows the meaning of the word nature and it seems the best fit with naturism is "the material world beyond human civilization or society; an original, wild, undomesticated condition". So naturist would be a person who practises being beyond human civilization. This is the view that we are trying to disassociate in non-naturist minds.
Nude by contrast is a simple term meaning to be unclothed. https://www.etymonline.com/word/nude.
It is clear to everyone what it means. It seems to me that naturism was used once the idea of sunbathing in public without fences (see the Welsh Harp incident of 1930) was abandoned and naturism became a secret world. Only those in the know would understand the word and other terms, such as sun club. As 'naturists' I think we are simply 'just being ourselves' - no pretence, no prejudice, no secrets.
I went to a talk by Prof. Alice Roberts yesterday - an interesting talk that explained that dogs associated themselves with humans 25,00 years before the civilised life of the Neolithic period (i.e. living in towns and cultivating crops) and were changing genetically as a result before humans began to select for the characteristics they preferred for pets. In it she pointed out that being a hunter-gather was a hard life.
So I think the term nudist is preferable and we should be thinking not of being 'at one with nature', but of respecting the forces of nature and rejecting the idea of man having 'dominion over the world'. Being naked is of course 'just being yourself' - i.e. not dressed up to play a different role.