I am continually and pleasantly surprised at our own thoughts' "syncretism."
I think we agree on the following points:
1) Catholics and Orthodox should not jointly pray with those who are not of their respective Confessions. This includes with each other. So joint prayer for the Pope of Rome and the Patriarch of Constantinople would be out, but I wouldn't be opposed to one charitably observing
the other's prayer or religious rituals, as long as it isn't active participation. I think both of our Churches agree with this on paper, but in reality it plays out differently.
2) We do not worship the same God that Muslims or Mormons do.
You know that Pope Benedict himself, when he was Cardinal Ratzinger, wrote that Assisi was pretty troubling to his religious sensibilities. Even at the time, he was rather against it. I would be willing to bet Hell would freeze over before anything like Assisi comes to pass under this blessed pontificate.