Umm, hospitaller wore black with white cross ? Not red with white cross. Did you missed it ?
The Hospitallers and the Knights Templar, formed in 1119,[4] became the most powerful Christian groups in the area. The order came to distinguish itself in battle with the Muslims, its soldiers
wearing a black surcoat with a white cross. The Order's practice of acting first and legislating later is epitomised by the fact that it was not until 1248 that the pope, Innocent IV (1243–54), approved a standard military dress for the Hospitallers to be worn in battle. Instead of a closed cape over their armor (which restricted their movements) they should wear a
red surcoat with a white cross emblazoned on it.[5]
