score:6
The Chicago Tribune has an article that proposes some theories on why the observation of the supernova went mostly unnoticed in Europe. The article mentions the significance of the date with respect to the Church:
Another reason the lack of records of the supernova is so puzzling is that 12 days after it first appeared in the sky, the Christian church began its final East-West split into the Roman Catholic and Eastern Orthodox Churches. Astronomical events were believed to foreshadow developments on Earth, making it unlikely that the appearance of a new star so near the time of such a major event would go unrecorded.
This source seems to imply that the contemporary sources who might have commented were silent on the matter.
The connection, however, has not been lost on everyone. This letter on fivedoves.com relates the two events intimately, though perhaps presumptuously:
In heaven, the Great Schism of 1054 AD is marked by a supernova explosion creating the beautiful Crab Nebula and witnessed visually by both Chinese and European astronomers. The supernova appeared visible to the unaided human eye during daylight hours in July 1054 at approximately the same time as the eastern bishops voted to remove themselves from communion with the Roman Bishopric.