Is this realistic when it's clearly really useful to have fire mages in your army, and other, not quite friendly cultures have no objection against doing just that?
Realistic for them to do? Yes. Realistic for them to do and survive? No.
Cultures do evolutionarily maladaptive things all the time. But then they get ground under by another culture that's not doing that. So you could certainly have an ingrained prejudice against these other forms. It would just be a severe disadvantage in any war against the other side, and that other side would use that advantage.
Which could lead you to a very interesting plot: a more secular part of the culture realising, no, seriously, we NEED to start finding and training firemages and earthmages and watermages and airmages RIGHT NOW before our enemies crush us completely, and having to struggle hard against the religious conservatives who are (and perhaps even with good reason, if you want to make it really interesting - maybe there actually IS something Wrong or at least potentially Wrong about the other four elements) dead set opposed.
But. It is entirely maladaptive, in terms of surviving.
Also, note: a split between "scientific" and "religious" explanations of the world is a modern, western-in-origin one. Even our own culture six hundred years ago didn't have it - there was all-encompassing philosophy, and then there was theological philosophy and metaphysics (dealing with god, etc) and there was natural philosophy, which observed the world around you. However, these were entirely united in their fundamental principals - and this is by far the more common way of thinking of the world, historically. So be cautious about necessarily grafting that split onto a world, especially one that may neither have the technological level to do so, nor any reason to, depending on how that world works.