Thanks for opening this very interesting topic! Then, let's begin the discussion. Here's my opinion.
The situation of Catholicism, Eastern Orthodoxy and Oriental Orthodoxy reminds me of the same divisions of st Peter, st Paul and st James. For this reason I hold the position of Paul, who did never cease to openly show his disapproval for the attitude of his fellow apostles, but at the same time never said they were heretics. Substantially both Peter and James were in error, and Paul hoped in a reconciliation. Did he ever celebrate the Eucharist with them once they doubted of the soundness of his doctrine? No, he didn't, but he always hoped for unity, and offered dialogue as an answer. Praying altogether for unity, in this case, is the first step to reconciliation.
I think the attitude of the Ecumenical Patriarch (God bless him thrice!) is a strange position, but he's not out of the boundaries of Orthodoxy, yet. I think that the blessed and all-lodable apostles Paul and Peter could easily have prayed together, kissed the Holy Bible and the Aramaic Gospel of Matthew with no violation of anything. Prayer is the first step for peace between the brethren in Christ... Even Jesus never refused to dialogue with the woman in Samaria, didn't he? But this is of course due to the EP's position, as he sees the RCC not as "heretic", but just as a "heterodox" Church which departed from tradition. Just a personal view, of course.
At the same time, I think the more "rigid" position of Patriarch Alexy II is more authentically Orthodox. His Holiness the Patriarch of Moscow (God bless him thrice!) is just doubting of the distinction between "heresy" and "heterodoxy". While I ordinarily think that before Vatican I the RCC was "heterodox", I consider post-Vatican II RCC as heretical too. The question of the Papal Infallibility is not just an error, it's a christological heresy as this recognizes the Pope the same condition as a second Christ.
That's why I appreciate the position of His Holiness Alexy II and at the same time can't condemn the very "positive" hope for unity expressed by His Holiness Bartholomew I (I hope he'll never go beyond these limits, though, introducing favorable positions on Papal Infallibility or the Filioque clause...)
In Christ, Alex
PS: John Paul II did even more terrible things kissing the Quran (an heretical work!) or denying any reference to the Promised Messiah to be truly present in the prophecies of the OT! What a terrible thing!