Nineteenth-century drawings of people praying at the Kotel show men and women together, so "tradition" suggests that this site has not traditionally been an Orthodox synagogue. People whose religious traditions are different from mine aren't therefore insincere. And differing from me may offend me, but I don't have the right to say "Your actions offend me and therefore you cannot do them." Moshe, I daven as you do. But if others find it meaningful and close to G-d to daven otherwise, it doesn't change my relationship to G-d or to the Jewish people.
from the article: Dispelling nine myths about Women of the Wall