One of my university modules last year involved looking at 1066 and it was emphasised that William the Bastard was given authorisation to carry the Papal banner with him during his invasion of England, showing that he had the support of the Papacy behind him.

However, I've recently been reading Thomas Asbridge's book "The Crusades" and in the introduction he details that until the time of Pope Gregory VII, any fighting and war by Christians was highly frowned upon, and that despite the idea of "just" wars (noted as being solely ones of defence) any and all bloodshed was, regardless, incredibly sinful.

So why did Pope Alexander II support William in his venture despite the fact that it was obviously going to result in bloodshed between Christians? I read somewhere (though I can't remember where) that it was potentially because English Christianity didn't adhere as closely to Catholic doctrine as the rest of Western Europe and so the Pope wanted to reaffirm Catholic power in the area. Was this the case?