I think the issue is that a clergyman may be told he should/can NOT pray in the name of Jesus.
In the military - a Chaplain may be asked to give an invocation at a secular event, (ie NCO graduation)
at the event, the Commander can inform the Chaplain NOT to pray in the name of Jesus, as it would
offend Muslims, possible Jews, ect. In this case - the Chaplain is not obliged to participate. (in a regular
chapel service - the Commander has no authority as to how the Chaplain runs his service)
Outside the military, the moderator could ask the minister not to pray in the name of Jesus. Again, the clergyman
is under no obligation to accept.
In fact, a few years ago, I was asked to give the invocation at a political event. I asked the Chairman if there would
be any problem if I prayed in the name of Jesus - and he told me it was fine. Had he told I could not do so, I would
inform him that I am not the minister he would need.
I would like to add this tibit. When I graduated NCO school, we had a Chaplain give the invocation.
During rehearsal - the Sgt Major informed us that we should bow our heads during the prayer - he than added
if we did not want to pray - then we were to inspect our shoes (at the position of modified attention) the entire time
the Chaplain was praying.
Likewise, If I were to be at an event that a Muslim were praying - I would simply inspect my shoes at modified attention.