I would like to add some prespective to this discussion if I may, from the islamic side, or jewish side.
Reading through the many posts I would like to summarized my points as follows:
1. Those who say men/women who refuse to train with the opposite sex are missing out, since this is a martial art and you dont choose you attacker in life, yes but who said that man or woman training has similar goals as the others? They could be training for the love of Aikido, not for the defensive tactics. They could be training for good health, etc. They are in a free country, they are free to choose.
2. Some say ''leave your religion outside'' and come on to the mat. Yet from the other perspective religion is part of them, its in their heart, can they leave their soul outside and come on the mat? Some would respond and say ''can you also stop the creator of the universe from watching us?" It is not like a T-Shirt you just take it off whenever u want.
3. As some members pointed out, not accommodating the special needs of members could result in discrimination against that member. Personally I would accommodate them to add perspective and diversity, yet as long as no hate and intolerance is spread. As a member pointed out on a specific case, some men/women wont touch the opposite sex not because of hate or intolerance, but because 1st of religious rules (no offense intended to anyone) 2nd it is part of their respect of the opposite sex that they do not touch them, ie. it is considered rude or insulting to touch a woman if your a man (its part of the religion's etiquette you can say).
4. The issue with Islam and intolerance. Doing some research I found that many so called Muslims act in the name of Islam and do bad things yet it is against the teachs of their religion, its a cover for them, and media projects it as ''Islamic''. For example, with the issue of the danish cartons as one member pointed out, the cartoonist's life was threatened. In brief, I learned that in no way or shape or form should his life be threatened by any Muslim, except the authority of that country who imposes the law. Its true that that cartoonist did an immensly insulting thing and gesture towards Muslims under the cover of freedom of speech, yet the ruler of law is the one who takes care of him not anyone else according to Islamic teachings.
5. I spoke to a few Senseis I know, running their own dojos. I have found that its an issue specific to the Dojo itself. Meaning, if their are more men than women, then a woman with religious restrictions can't practice there, yet if its 50 ; 50 , then they could accommodate her partnering her with a woman. Again, it depends on the Dojo's situation. Yet what worries me is that some instructors will be hard in they way they turn down these people's requests (what ever religion they come from), and then the person turned down would associate that rude rejection with how Aikido operates and attitude it carries. After all instructors are representatives of Aikido. I personally have seen instructors who were rude in turning down special accommodations because of that instructor's own perspective or beliefs, not because he or she can't accommodate a student. I know students who grew more in respect of an instructor because that instructor turned them down with a smile and politeness. After all its all about peace and harmony!
Finally, I would say its an issue of dialogue and understanding the other side's story. Its up to the dojo and instructor and their special situation if they can or can't accommodate. But my wish is that an instructor takes the time to understand the student. Who knows that student could be an asset in the future, bring in diversity, perspective, and harmony to the class with his uniqueness.
Enjoy Aikido and have fun, relax