The US Military's only Messianic Jewish chaplain is profiled here. Long time FailedMessiah reader and military man Brian Kresge notes the potential problems with having a Messianic Jew serve as a chaplain.
Does the military consider this chaplain to be a Jewish chaplain? If it does, I think we should object. If it does not, and classifies him as Christian or as a separate stream, I don't think there is much we can do.
[Not to be overly cynical, but I do not think this is the only messianic chaplain in the US Military – Chabad rabbis serve as chaplains. The theology is largely the same – only the name of the messiah has been changed. Christianity started out as Rebbe-centric Judaism. People tend to forget this.]