Splitting hairs over halachical rulings is of no importance. This is Israeli sovereign area and anyone willing/wanting to visit should be able to do so. If the followers of the pedophile degenerate Mohammad don't want anyone inside their abominations (as long as they're allowed to remain) then it's their call. Religion has nothing to do with this whole issue. Taking charge has!
The fact that they dress so very ultra Orthodox and listen to their chosen rabbis does not mean that the halacha that they tout is really the halacha.
Halacha is composed by many opinions, pro and con, and not something that one group can say that his rabbi is the greater scholar and therefore the halacha should be as he says.
There are many opinions on this and it is not simple for us to decide, but rather to realize that it is NOT decided by the length of one's beard or peyos.