Contrary to what you might have expected, this will not deal with religious extremism, but why we shouldn't use the term. It's something I have never heard anyone on TV or elsewhere ever mention. When you hear "religious extremism", typically, and more than that, every time, it's about something bad. A "religious extremist" is someone who kills people for his or her cause. If you haven't yet guessed why I think this is a bad term to use, here's why.
Better than the "religious extremist" is the "moderate" religious. What is very wrong with this is that those terms imply that being more into a religion is bad, and if you're only half-assed, it's better. But mostly, it implies that religion is essentially bad and thus, it's better to be "moderate" than "extremist". I don't like that terming because it subtly adopts an ideology in which any religious behaviour is negative.
"Religious extremists", very often, aren't even religious. Depending on their religion, of course. But take Islam or Christianity, both highly condemn murder and the loss of human lives; a "religious extremist" who kills for either is in fact a big sinner regarding either faith. It'd be ok if we thought that the extremist was merely extreme, and happened to be religious too, but it's not so. It's not so because the "moderate" ones are moderate not in their murderous acts, but in their faith, and that's just wrong. If you're a good religious person, you will not seek to do things in a half way like it doesn't matter, you'll do it to the full, and that means, for either Christianity or Islam, that you will NOT kill people. It's only if you're "moderately" a believer that you will think yourself allowed to do things against the faith you supposedly believe in. So, in that configuration, the extremist is the one least likely to kill innocents because it's against their religion and belief.
Now, I'm not suggesting that we should change the terms, because habit is stronger than reason and we wouldn't be able to change that unless everyone made an effort and everything, which I don't think will happen. My point is that, subtly, we speak of religious people in terms of being "more" or "less" part of something, and that if you're "more" of it, you're liable to kill children and blow yourself up. Not my idea of religious behaviour.
I think this is an important point because today more than ever, religious people are under fire from every side of everything and in general, if you're religious, you're thought to be either stupid, gullible, naīve, or a dangerous sociopath. And I forget narrow-minded and everything. I'm slightly upset by this because it's the complete opposite of what a religion really is in nature. I cannot generalise over all believers of all religions, but it does take a massively open mind to even consider the possibility of there being a God when for years you have thought this was a very foolish idea.