Secondly, the issue is not your beliefs, unless sharing a meal with a non-believer in Christ is a violation of your faith.
Thridly, trere are thousands of chaplian, priest, ministers, and rabbies that routinely officiate at inter-religious ceremonies. No problem ever arises on Capitiol HIll when the Chaplain leads in a prayer there.
All these people are Christian, educated, and even ordained. None of them betrays Christianity.
It's not about one's beliefs: it's about tact and unity.