Many WOW members are from the Modern Orthodox community, and my understanding is that they see themselves as part of the “Women Prayer Group” circuit. If they’re not given this attention, and are allowed to do as they wish at the Kotel, I don’t see how that will affect any of us.
As far as the organization goes, once they stop taking funds from the New Israel Fund and start fighting for the right of Jews to pray on the Temple Mount, I’ll have a less bitter view.