Church militants of the Empire

Does the Empire have church militants and church-affiliated soldiers? Bishoprics, templars, crusader kingdoms, glebes, monastic orders, brotherhoods of holy warriors, fraternities, dueling cults etc. If the Empire does contain such groups, how are they structured and organized?

Did the medieval-era Eldrae societies have inquisitor and witchfinder-equivalents? If that is the case, do they still have similar institutions?