I don't feel particularly relevant (cis here) so feel free to ignore me but I find it a super interesting thought exercise, maybe these two have shapes that are ambiguous enough to qualify: 🌺, 🌽?
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Guess 🍑 is kind of generic, after all, who doesn't have one?
The ⚧️ Transgender character is kind of an "all in one", but its meaning is more about gender than about the genitalia symbols it's made of.
The ☯️ yin yang is a representation of balance, among other things of the feminine-masculine.
As mentioned, the 🌺 kind of evocates genitals without specifying which ones, but it's rather associated with female ones.
In polyamory, there is 🦄 and 🐲, but they again refer to particular concepts that may not be what you wish to convey.
I don't think there is a single emoji unequivocally meaning "erogenous zone" without some gendered connotations. On the bright side, nothing is stopping you from using whichever emoji or combination you want. Sexuality is a conversation, it isn't a one-fits-all, and you are allowed to ask or offer further clarification.
When in doubt, 👄👅😏♥️... 🃏🌸
In regards to your asterisk, I might call it puritan. In terms of emojis, there isn't one I know of in Unicode that represents genitalia in general, perhaps a custom gif that's added to your chat groups and communities would work?
puritan
Ooh. Good. "Victorian" also comes to mind, now.
EDIT: I rather like "victorian" because it's secular and more recent and has the right connotations suggesting how contrived the very concept of "proper" sexuality is – and how absurd. I fear that "puritan" might get bogged down in concepts of religious phobia and zeal which are certainly appropriate but could be a distraction – it's adding trees to distract from the wood.
Maybe🍡 as it could be a wildcard for a penis, vagina, or both
I want to propose the tomato.
In some languages, tomatoes refer to the testicles, while some people use it in similar way to mean the "passive" organ (vagina, ass). It's also a very versatile fruit with many different shapes.
I usually use typical or conventional instead of traditional, normal etc.
Edit: You could probably also use normative.