At our community senior men's club we have invited clergy do the invocation at our semi-monthly luncheons. The clergy are from a variety of Christian denominations, and I also recall a Jewish rabbi, a leader from the Bahá'í community, and a Muslim imam.
Because it was a lot of work to arrange for invocators, the leaders have now opted for having a Roman Catholic deacon who is a club member as the permanent invocator. This is neither ecumenical or diverse. Our organization is not Catholic, or even Christian, although most members are Christians to some degree. My pastor suggested we might have volunteers from our membership as invocators, and I suggested that we do that, regardless of a member's faith. Non-Christian invocators would make Christians feel a little awkward, but it seems only fair.
Serving as an invocator gives a Christian an opportunity to witness to others, but how do we do it without giving offense? I've heard that some don't close public prayers with "In Jesus name we pray," or the like, because that offends some. What about that?
On the other hand, there was a recent news story about an invocator who sparked outrage by reportedly invoking the name of Jesus numerous times and also doing some editorializing on a "hot" topic, both of which were offensive to several in the group—evidently not a good witness. Some Christians were offended, too, and I'm offended when our deacon invocator, after his traditional closing invoking the trinity, shouts, "Let's hear it, men!" and many of the men loudly respond, "Amen!" It seems to me to be disrespectful (and not like the responses in some churches with more audience responses than a traditional CRC).
There are several questions to explore here, and I hope my post isn't too complicated.