James Chye wrote:
I know that the basics of aikido can be taught and learned without mentioning the religion of O-Sensei, just as the basics of physics can be taught and learned without discussing Newton's experiments with cylinders.).
I would really compare it with having to know what religious beliefs Newton had to understand how he developed the theories. Sure it must have had an influence, but it doesn't mean that understanding it is in any way dependent on knowing his religion.
Admittedly I was one of those who James suggested leapt onto their soap-box. And doing aikido has undoubtedly opened me up to eastern philosophy. However, although changing someone's perception to enable aikido to be understood better may be useful (e.g. discussions on yin/yang) - I don't think omote-kyo as a specific religion has any relevance for understanding aikido - only for understanding Ueshiba.
Personally I agree with Ueshiba, when he said "aikido is a flower that just happened to bloom in Japan".