Ask your Priest
Better yet watch your Priest. See what happens when you are in a situation where common prayer among a variety of varying heterodox is being held and he is present.
Once, we were among a crowd that obviously were rather charismatic. My Priest turned to me and said (with a touch of humor): If they start holding hands and swaying, don't you even think of grabbing my hand.
I asked my Priest directly once (and I've mentioned it here) about closing AA with the Lord's Prayer. He gave me his NBD shrug.
Funny thing is that it does "feel" different saying that prayer in that context. Strangely, more "ritualistic".
I try to remain respectful: silent. But I won't hold hands, sway, mouth the words, say "amen" etc. If the prayers are Orthodox: Lord's Prayer, then I have no problem really.
And FWIW on the Lord's Prayer, Fr. Hopko believes no one should be saying it who ain't Baptized and Chrismated and regularly communing with the OC in an ideal world.