I thought it was perfectly reasonable myself. The machine will only respond to a pairing of XX and XY chromosomes, much like how reproduction occurs.
The exception is the intersex pilots of the Nines. This ties neatly back in to the Stamen/Pistil designation of the male/female pilots respectively, and thus is also a reference to how plants are both male and female.
It's all a comment on the basic building blocks of life, and how, without both the male and the female components being present, new life (in this case represented by the activation of a FRANXX) cannot be brought to bear.
I think it's very clever.