(Slightly adapted from a not-entirely-serious blog post.)
We're all used to ♀ and ♂ symbols for "female" and "male", and their corresponding pairings (⚢, ⚣ and ⚤). (We are all used to that, aren't we?) ⚧ is also becoming an increasingly familiar symbol for "trans", and it appears to have won out over ⚦ and ⚥.
Does Unicode supply us with a nice symbol for "nonbinary" where ⚧ is not entirely appropriate? Well, yes and no. ⚥ can also be used for "hermaphrodite" (in entomology), a simple ⚪ stands for "asexuality, sexless, genderless", and ⚲ for "neuter". But this doesn't cover anything like all possibilities, and here's no umbrella symbol (other than ☂).
However, CN Lester's article Non-binary gender makes me free, not a traitor is headed by this:
and if you accept that the symbol in the bottom right is ⚲, there's one more symbol there: ☿. If you don't recognise it, it's the symbol for the planet Mercury, or the alchemical symbol for, er, mercury. To go with Mars (♂) and Venus (♀). To be [gender-]fluid.
Could this be what we're looking for?
All symbols used in the text come from the Unicode Miscellaneous Symbols block. Note that this erroneously refers to all three trans symbols as being for "transgendered sexuality", and I've already had someone volunteer to take on getting this corrected!