okay under theocracy: the state doesn't let outside missionaries convert. also the state doesn't spread non state faith. however you can make missionaries of minor faiths - I did this - and use them to spread that faith within your realm. you can also switch between them if spiritual convert several, and then switch back. cities can be multifaith. they still count for any faith present. if all are jewish and christian, you can be jewish or christian and get bonuses for either [and you could be gandhi to do it as well!]. the main benefit of theocracy is the +2 xp of units with state faith. if you combine that with feudalism's vassalage gives you +4 xp of units in cities with state faith. add a barracks for +4 xp, and that comes to +8 xp for each unit made. now, when you get military tradition, a unit of 5 or more let's you build west point that gets you +4 xp in that city. with assembly line, you could build the pentagon giving you +2 xp in all cities.
okay lets add this up if you have vassalage, theocracy, and barracks in all cities, and the pentagon, and west point. and state religion in all you cities as at least one of the faiths in each:
+10 xp in all cities - the west point city gets +14 xp upon production. that's a quick advanced training program for your military. add to that line of site advantage if you found a faith of nation you intend to invade that has most cities with same faith. and if you are in this situation, build a shrine and their cities continue to earn you gold even during war!
there are other advantages as well.