The Army is VERY AWARE that their job is ultimately to kill the Queen's enemies. Acronyms are used for the same reason that drill is used, for the same reason that doctrine is used, for the same reason that "DESTROY" has a 40-word definition in the Army Field Manual: so that when you're cold, tired, exhausted and under fire, you do the right thing and the thing intended by your commanders.
There are people who kill others for not being of a certain religion. They do not wear the UK or US flag on their shoulder. In fact, you'll find that there are many different religions - and atheists - in the UK and US armies. Remind me again, how many Christians, Buddhists and atheists are in the Taliban or Al-Qaeda?
(I'm in the Army. My job, when I'm not socialising in mess dress, is to move supplies about. And kill people who try to stop me).