Women should not be allowed the vote. There is no reason they should not be able to run for office, though, as they would be competing with men for men's votes.
This, of course is an aggregate. Individual women don't fit that but you can't select the electorate by individual psych tests. It must be done in easily identifiable categories, such as all male adults, or all owners of a certain amount of property, et al.
I practice a lot of employment law and I can tell you that the biggest reason women make less than men is that they do not negotiate up front. Women tend to take what they are offered, then complain later. Women tend to stay in the same position longer. Men tend to argue for a higher wage, and move on to another employer as needed. (I am talking about educated professionals.) That says to me that women value security, which is costly, but which makes sense when it comes to reproduction. This is so innate to the way the sexes view each other that this wage gap will never change. And this is not to mention the time off created by child bearing and family care, which everyone expects of the daughter and not the son.
I have also noticed throughout my 35 years of a professional career that no one ever asks what I do for a living, even in a professional setting. They always ask my spouse.
Last, I have noticed that there are very good reasons that men should step aside for women and hold doors open. I have been mowed down by those larger and stronger than I for years. I cannot compete for a place in the elevator against an 18 year old male.
Clearly my gender determines my opportunities which make them very unequal just based upon the form and function of my body. If we rail against this we complain about the standards of God, and this is why we find ourselves without any standards at all in the end.