Agudath Israel and Chabad are two organizations whose members do not engage in ecumenical exercises. Chabad, of course, is a pioneer at publicizing the Sheva Mitzvot Bnai Noach, but now almost everyone Orthodox is on that bandwagon.
I'm willing to believe that Agudat Yisra'el doesn't engage in ecumenicism, but I'm not so sure about CHaBa"D, if for no other reason than they are so prominent, especially in encouraging public celebrations of Chanukkah (which is a good thing when it isn't misunderstood).
Unfortunately, the Chief Rabbinate of Israel has been a disgrace in its ecumenical activities, as have the Jews of Rome (where the Pope might as well be a member of the congregation). And of course, "Modern Orthodoxy" is the absolute worst of all (discounting heretical "branches" completely, of course).
The Chief Rabbinate of Israel is a political entity and does the bidding of the secular government, at least as much as it can get away with. A Chief Rabbi will be respected or ignored based on his Torah, not on his political appointment.
You really don’t see the difference between a Chabad Chanukah outreach and an ecumenical meeting?
Here’s a clue: If one group is in charge and is teaching the other group on a one-way basis, it’s not ‘ecumenical’, even if adherents of different religions are present.