I think Crusades/Jihads can happen early if a different religion takes over a place that it's not meant to be in. Like, Byzantines expanding into the Middle-East or the Spanish Muslims expanding into France
Yes, in vanilla, if the Christians don't control all of Rome, Provence, Toulouse, Paris, e_byzantium, Constantinople, Ancyra and either Athens or Corinth, the Christian crusades can start at any time. For the Muslims, it's Jerusalem, Mecca, Baghdad, Damascus, Cairo, Marrakesh, Tunis, and Al Djazair. The Pagans can't start until one of the other 2 do.