To me, it feels like the shadow pan are similar to a wooden sword coated in a thin layer of steel. They appear to be strong, they flash prettily in the sun and with enough force behind the blow they can even kill. They are however easily broken when hit by an actual steel sword. Don't get me wrong, the Shado-Pan certainly have their moments as have been mentioned a few times in this thread (Townlong and books for example) However the bottom line that I personally take from their story is a reinforcement of Shaohao's sins.
The Shado-Pan are too proud, as are some elements of player factions, and as such were easy prey to the Sha when they manifested in force for the first time in ten thousand years. I completely understand that this was a stronger manifestation than they were used to but in my eyes this is a poor excuse, when your entire order is dedicated to controlling their emotions with an iron will it should be a source of great shame for any amount of external pressure to break that calm. This is further reinforced by the fact that SOME elements of the Shado-Pan were indeed strong enough (i.e. quest givers in Townlong, Shao-Pan monastery) in addition to many other groups being strong enough to resist, players, Mogu and Zandalari for example. The Shado-Pan have an over-inflated opinion of their prowess based on the fact that they have had very little actual challenge in living memory and therefore like Shadohao himself fall prey to the greatest of sha with ease.
Regardless of my personal opinions of the Shado-Pan as an organisation, the topic is I believe regarding whether they are justified in their hate of the horde, and whether they could take the shrine? To those I would respond with yes, their hate is justified and I doubt anyone would argue that. The Shado-Pan could certainly storm the shrine, but if and when the horde decided to take it back they would have literally no chance (similarly the alliance could obliterate the Shao-Pan with ease) The Shado-Pan are not trained for war, they are trained to control their emotions and defend Pandaria, this is very different to the kind of war the Alliance and Horde are capable of unleashing if given cause.
That's my opinion on the matter anyway, I certainly concede the Shado-Pan can be interpreted differently to my view.