I don't see how Native Americans can object if you wanted to implement this for the practical effects it has and discard most of the spirituality attached to it. However, excuse me for being cynical, but I don't think that's what you want to do.
Also, what iron jones said. This is quite clearly discrimination with respect to women, and you would need a
really good reason for it to be implemented in our society. I'm not sure which "way" it is discriminatory, but even attempting to implement the idea poses a huge cost to businesses and men. (Not to mention pressure on women to not use it.)
As for the "sacred" role women play:
we are all sexy, sexy Von Neumann machines.