Thank you all for the interesting discussion here! I would just like to share some thoughts that occur to me when reading this.
As the discussion shows, the way the Sangha has been established is clearly built on a binary view of gender. There is the Bhikkhu and the Bhikkhuni Sangha, and someone willing to ordain has to somehow fit into one or the other. This binary view is also reflected in the Buddha’s famous statement about his mission, namely to establish the fourfold community of disciples, both male and female monastics and lay practitioners. The idea that gender can be other than binary did simply not exist at the time, and didn’t indeed until very recently.
On the other hand it is also very central in the Buddha’s teaching that gender as such doesn’t matter much for the practise of the path, and even for those who are not interested to practise anything gender isn’t in any way fixed or permanent. Are we allowed to conclude from there that the binary way of setting up the Sangha is nothing else but a compromise to the way gender was perceived at the time? That this very fact of having a binary Sangha can be considered as one of the “minor rules” laid down by the Buddha that can be abandoned after his passing?
Today we live in a society where gender isn’t strictly binary any more. Maybe for large parts of the population it still is, but there are this kind of discussions now, and there are (and have always been) the people who just can’t fit into the binary system. What to do?
In order to do justice to this situation it would probably not be enough to establish a genderless vinaya as proposed by Ayya @vimalanyani in her thought experiment:
Let us just take the thought experiment one step further: Do we need a genderless Sangha and a genderless ordination ceremony? Maybe there is even a precedent for that in the EBTs: The “come, … [name]” ordination.
Sure, not many monastics (and laypeople) living in the world today would consider this as a valid ordiantion… but just dreaming! 
