The pilgrimage of 1844 brought hundreds of thousands of people to Trier over several weeks, and it produced a schism. Johannes Ronge, a suspended Silesian priest, published an open letter attacking the showing as superstition and the bishop who ordered it as its promoter. The letter circulated widely in a Germany already politically restless, and out of the response to it came the German Catholic movement, a breakaway that drew substantial support for some years before dispersing. A relic showing had become a political event because it offered a public occasion for arguments that had nowhere else to go.
The other difficulty is a rival. The basilica of Argenteuil near Paris venerates a tunic said to be the same garment, with its own tradition of arrival, its own showings and its own following. The two claims as traditionally made cannot both be true. The harmonisation sometimes offered, that one is the inner tunic and the other the outer cloak, is a later reconciliation rather than what either tradition originally said, and it satisfies few people on either side.
The atlas records both claims and endorses neither. What is not in question is that a garment has been kept, guarded, argued about and travelled to at Trier for eight hundred years, and that is a fact about religion whatever the cloth turns out to be.