OK Where to begin? For one, The Kotel is not "for everyone", it is a Synagogue, just like you wouldn't like if a group of J for J set up shop in your Shul, why should the people Davening at the Kosel have to tolerate the WoW?
I'll agree with you on the point you made that the way the protests are being carried out is counterproductive. But you assertion that we should "equally accept" and legitimize "all branches of Judaism" is wrong. I respect every Jew, and don't care what they do in their private life, as long as they don't call it Judaism. Judaism is not a democracy, it's a religion.
What does that mean?
Shulchan Oruch says otherwise.
Even if you can't do anything about it, and you can't even say anything about it, you could at least care.