I was an Orthodox Jew from birth, but as an adult I grew away from the restrictions because I found them to be the mechanations of men acting out of their own earthly motives, not ones of divine enlightenment or direction.
When I first trained in aikido, I was hesitant to join a co-ed class because of the contact with males to whom I was not married. But I came to realize that if I wanted to integrate myself into the greater outside world and culture, I would have to adapt to it and not expect it to adapt to my rather limited and limiting little enclave of medieval holdouts.
I'd have to say that getting into martial arts was my first step in opening up my mind. I don't feel that it has made me less of a Jew, just way more sensitive and aware of what constitutes being a Jew, and what is artifice created by those who would consdier themselves the ruling class. The choice of whether to train or not has to be based on the comfort level of the individual. He (or she) can always find someone to start a single-sex school.
As for women in the dojo. I have no trouble with the OP. I train with women all the time in my dojo-I just make sure to shower after.
I'd think that those women would wish that you showered BEFORE you train with them. [crinkles up nose]