Here in Japan, the only separate sex aikido dojos are those attached to single sex private colleges, where the general public are not admitted anyway. There is one women's class in the Aikikai Hombu, though, interestingly, the instructors are male despite the fact that there is a female shihan in the Hombu's Shidou-bu.
I have never come across a dojo of the type that Mr Linden runs and even the Founder had women students in the Kobukan Dojo, who trained on an equal footing with the male students.
I would also think that even the notions of personal freedom might well vary with the culture. Though the notion of human rights has come more into prominence here recently, I think that the idea of individual freedom based on a certain concept of the individual to do as he or she wishes is accorded some lip service here, since Japan considers itself democratic, but is not really deeply ingrained. This does not, of course, affect Mr Linden's freedom to run his dojo as he wishes. Simply, it might be more difficult for me to do something similar here if I wanted to.
In any case, I personally believe that is essential to aikido training that men and women train together. Physical differences have an obvious effect on training and it is essential that both sexes become aware both of these differences and how to deal with them during training. My dojo population is currently about 50/50 male/female and everthing works very well.