Various Faiths often come together to pray at secular events - Veteran's Day Memorial in a park, commemoration of some national atrocity (ie. 9/11, genocides, etc.), political swearing-in ceremonies, graduations, etc.
Laity often pray together at various ceremonies - (all the above), plus school events, sporting events, hospitals, etc.
I do not believe any of the above is harmful in any way... as long as the clergy do not attend and venerate sacred objects of any other Faith. For example, the Pope kissing the Quran in my opinion was wrong... because that added validity to the Islamic Faith.
The same would be true of any heterodox clergy (or laity) partaking of Orthodox Sacraments. They are free to kiss our icons, cross, relics, etc... but, not the Sacraments.
If laity partake in personal prayer with heterodox, it is a mixed bag. I once found myself in a very stressful situation in a hospital... and I was sitting in the corner of the waiting room in tears, prayer book on my lap... when a family of Evangelicals felt the need to comfort me... so they all sat down around me... bowed their heads, took my hands... and prayed to the Lord Jesus Christ.
Knowing the prohibition of praying with non-Orthodox... I was actually at a loss of what to do... Do I tell them to go away? No. That would be rude. As we are taught to eat meat during Lent if it is offered to us, in order not to insult our host... so, I believe praying with these good-hearted people would be acceptable.
However, going to someone's house for a Seder, or to break fast during Ramadan... well... again, in my opinion... that would not be good... because with our presence we would show acceptance of validity of their Faith.
I even refrain from wishing people Happy Eid, Happy Dawali, Happy this or that... because I do not recognize those holidays... I do wish them an enjoyable and safe weekend, or day or whatever...but, do not specifically call out their celebrations.