Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh.
It is permissible for a Muslim to make supplications and respond to supplications recited by followers of other faiths provided that they do not involve calling upon anything besides Allah or contain idolatrous phrasing.
The participants in these discussions should agree on certain ground rules, including not infringing on participants’ particular beliefs and convictions.
As far as common activities held by followers of different religions, those activities which fall within the category of rituals which Islamic Sharia requires to be performed in a prescribed format offering those rituals in a way contrary or variant to prescribed forms is an act of innovation which is not acceptable in Islam. For more details, please read my paper which was written on this topic at the following link:
Almighty Allah knows best.
Views expressed by hosts/guests on this program (live dialogue, Facebook sessions, etc.) are their own and their appearance on the program does not imply an endorsement of them or any entity they represent.