Filthy ecumenist chiming in! Let's all get to together in a Jesus lovefest and cast down all the barriers that divide us. Okay, so many some of those pesky "traditional" doctrines like the Trinity will have to go, but it's all worth it for the glory of the New One World Order, ruled by Our Dark Lord the Antichrist Pope Francis!!!
In all seriousness, the "ecumenism" that I subscribe to is the same brand that others have mentioned: we never compromise the Faith for others, but we should be respectful to them. We don't disregard their differences or try to explain them away, but we don't go around condemning people as schismatics or spreading filth about them to bolster our cause. Like it or not, we do live in a pluralist society, and one of the positive aspects of that is that in most parts of the world you can go on a lunch date with someone outside your faith without being slandered as a heretic sympathizer, if not an outright heretic. Essentially, the ecumenism I support is being a decent human being and not calling people out every second for what they believe.
Now, when it comes to specific theological discussion, I don't see anything wrong with just explaining your beliefs to someone and letting them explain theirs to you. You're not devising a way to synthesize the two systems, you're just getting everything out on the table in a polite way. And it may be that over the course of many such discussions, something might happen. Maybe one side realizes they were wrong. Maybe neither one changes their stance but they reach a consensus that they both believed the same thing. Great. But none of that should be the purpose of an "ecumenical dialogue," which is simply an ongoing dialogue in which both parties feel comfortable speaking to one another.
I guess I don't really foresee much happening from my brand of "ecumenism," but that's not the point. I just would like to think that we can live in this world without tearing apart the people who are much closer to us than we probably realize. But that's just it. It's often those closest to us that we tear apart for not being the same.
EDIT: Also, who the heck would vote "OO & RC only." If you're an RC who doesn't want to talk with the EO, why try the "monophysites" who denied even more of the Pope's ecumenical councils? If you're an OO, come on, man, we're way closer to you than the RC. You can't just skip us by. Not cool.