So then what better name could one have for the parts that textiles strive so hard to keep covered, (whether they be their own or those of others

I suppose we could use the term "banned parts" because most of society seems to see it that way, but then God does not ban them nor would I care to call them that, as to do so is to call good evil and evil good,(Ref Isa 5:20).
"Wobbly Bits" has some validity but they are not always so as various of them may be firm, and dangling bits does not work all that well for the same reason, and implies feebleness.
It is rare to find a person who does not strongly value such parts. It has been the prudishness of the world that has led to us hiding these parts and making up euphemistic terms that seem to belittle them and attach shame to them, or at the other extreme crudely brag upon them for irrelevant reasons (e.g. excessive size or prowess of performance). Actually using the words of a dead language (Latin) to refer to them does not really help either.It would be nice if we could find a term that meets the criterion reflected in 1cor 12, where Paul wrote: 23 And those members of the body, which we think to be less honourable, upon these we bestow more abundant honour; and our uncomely parts have more abundant comeliness.
"Gender Parts" might be a useful term, more so than say "Genitals", as for instance "breasts" and the "anus", are consider private parts and they have no function that is "Generative" per se (i.e. capable of generating a new life) albeit that the lactating breasts to promote young life.
Coming up with a term that is not a prudish euphemism or distant technical Latin is not easy.
"Gender Parts" pretty much works for me, but some may object that it excludes the anus which is pretty much lumped among the concept of private parts based on the use that some put it to. However some states seem to now have laws that define the"gluteal cleft" as a private part so that bikinis would technically be regarded as exposing a private part, and then of course there is the matter of the classic "Plumber's Crack"
I suppose that we might seek some expert linguistic help on this one ........(e.g. Petros/Celcius)