I recall there's a strict protocol for sacrifice that applied to the second temple but I can't cite the correct lit. How does an M.P. rate to perform a sacrifice? Uri's name is not Cohan either. This guy is rousing rabble, imo, because the Moslemi are gonna go nuts about it.
The High Priest, a single person, needs to be a Kohain, not be named Cohen. Leviim and Yisraelim may attend but cannot be a High Priest.
A Rabbi may be drawn from any one of the three. Only the High Priest must be a Kohain..and that was during the existence of the 1st and 2nd Temples.