Brits must look at this differently than we do. Conscientious objector status isn’t uncommon among those in the medical services in our military.
Odd that those who refuse to use a 'gun' to kill because of the Hippocratic Oath don't seem to mind using a pair of scissors and a vacuum cleaner to kill babies in the womb, or approving of other doctor's doing so.
When there is conscription in place, the British military does allow for genuine conscientious objectors to serve in non-combatant positions. This has been the case since World War II (technically since World War I, actually, but the World War II system was much more effective and organised).
But at times when joining is completely voluntary as it is now, the situation is different. The position is that a conscientious objector simply should not join the military.
There is a procedure in place for somebody who becomes a conscientious objector after they joined to continue to serve, but they have to convince a panel that their change of heart is genuine. In the case of this man, it was decided that it was not.