Think of prayer as a time of deep reflection, meditation, and spirituality that people of all faiths share. I have Christians and Jews in my family and we pray together all the time when we're around each other. "A family that prays together stays together."

We do such things as referencing God but not Christ so prayer can be an inclusive venture. "Thank you for this gathering...we pray for strength (to what or whom they pray is their business)..etc.." When you create a prayer, read it to see if someone could guess what "religion" you subscribe to just based on the prayer. If they could, revise your prayer to be less "religion" and more "spiritual."
rant/
This is not an issue in every collegiate and graduate chapter because some chapter members are so close that they do know someone's professed faith, including chapters that attend religious services together. That can also have to do with the majority religious demographic in an area. However, when the religious and faith demographic of the chapter knowingly changes, they should make the necessary adjustments without making anyone feel left out. For the record, part of this involves steering away from statements like "XYZ is an organization based on (insert religion) principles" unless there is hard evidence to that fact. /rant