You are right, but Christof's clothing (with the red cross on the white tissue) remembers A LOT of the Poor Knight of the Temple of Solomon - the Templar Knights, and the order was largely known and spread in the age of the Crusade, because they gained a lot of popularity for their value in battle (at least before 1307), more than any other order.
Yes, it is true, but Templars was the most wealthiest and richest order in the Christian world, although the members of the Order was really poors and modests. In the Western Christian societies, they had exclusive rights to usury, and this right gave them too much control and power upon the European kings and their noble Vassals. Although the money of the Templars was in good hands (Templars protected the pilgrims, handycaps, willows, orphans and anyone!), the promise of too much many makes too evil the men - especially the kings in Europe. (See Philip the Fair's direct persecution against the order in France...)
One should also say that the templar clothing shows a red cross on the left side of the chest, near the position of the heart, but this is often ignored by everyone, so.. :0
Yes, it is also true. Templar Crusaders also used the Red Cross upon their White mantles, but there is a different between the Templars' Red Cross and Christof's Red Cross. Templars' had a special Red Cross (see below) with a different shape of cross. Additionally, after a time, the color of Templars' cross has been Black.
(http://www.housemorningstar.com/images/161_CrusaderTemplarCross.jpg)
Christof was neither a knight of St. John, nor a Templar knight. If Christof weared his Red Cross upon a White mantle and he would be a Templar knight (Templars used Red Cross. Knights of St. John used generally White Cross upon their Black mantles) this would be a sign of his Cleric status, because in the order of Templars, the White mantle was a sign of the total sanctify. Laic member of the order of Templars' also weared the Red Cross, but upon a light-Gray mantle, instead of the Clerks White mantle.