I came across this comment on another site of the Stack Exchange network posted on a question discussing whether it is OK for someone who is not a Christian to be participate in a Christian prayer (saying grace):
I'm Jewish in the Christian-dominated US, and even though I'm not deep in the bible belt I run into "of course you are; isn't everybody?" presumption quite a bit. As a Jew I am forbidden to participate in prayers to anybody other than our God, and that poses difficulties sometimes. Your advice to just step back if standing or silently shake your head to the people on either side if sitting is what I do. (If I can avoid being at the table I do that.) That works for me, and I find that nobody takes note of my failure to say "amen" (or any part of the prayer), either.
My (admittedly limited) understanding of the relationship between Christianity, Judaism and Islam is that the three worship the same God. Each approaches their relationship to God differently, but the God is the same. Wouldn't it therefore be permitted for a Jew to participate in a Christian prayer as long as that were directed to God and not to Jesus Christ?