I agree 100 % that prayer is between the individual and God, it is indeed a private conversation. Prayer is a bounty for our soul.
In the Baha'i Writings Congregational prayer has been taken away. (There is a couple of exceptions). So in Baha'i Houses of worship, at a set service, prayers are offered from all Faiths, by a selected individual.
I personally, when I choose to go to the church, listen to the congregational prayers, but say it internally with my own heart. It may appear ignorant to those that witness the silence, only because they do not see my heart.
The same with the eating of bread and drinking of wine. I do not participate, as this ritual has been removed in the Baha'i Writings, but I am speaking in my heart of the knowledge of God when they partake of the Bread and I am enraptured in the Love of God, when they drink the wine.
I hope this self reflection, offered in Love, shows how some one who is praying in a different Faith, is not necessarily praying to Idols, nor a different God.
Of course this can be discussed in many ways, and that is the issue with Internet chat rooms, misunderstandings do not have immediately clarification, and the personal contact, so Important to communication, is not a available. Maybe one day this may not be the case. We may be in virtual chat rooms.
Regards Tony