Except the Sharansky compromise is mixed davening. Surely you won’t advocate mixed davening at the Kotel?
It’s in a different section. If I could stop mixed davening anywhere in the world, and certainly at the kosel, I would. But if it is in a different section and doesn’t infringe on us at all, I suppose I can deal with it if I need to.
The same way I deal with the avoda zara on top from the moslems, I can deal with their avoda zara. (Not exactly: Islam is much closer to Judaism than they are.)