There are a lot of common avenues of arguing about Church music that I think are seriously flawed and particularly destructive because they may be arguing for the right music for the wrong reasons. Here I'm simply outlining the ways I think are particularly unwise—perhaps in another place I can begin to outline the ways I think one ought to do it. (The bold affirms what I do not.)
1. Church music must be old. I've addressed this a bit already, but let me restate here. All music is, in a fundamental sense, traditional. It simply depends on what tradition you're plugging yourself into. Any contemporary Christian artists or praise choruses are doing just that—plugging themselves into musical traditions. Similarly, it did not take a thick layer of dust on Bach's manuscripts for his music to become traditional. His music was traditional from the moment he wrote it. It was in the tradition of Praetorius, Schütz, Pachelbel et al.
This is also a theological point. Most famously, but certainly not the only instance of it, Psalm 98 enjoins us to sing a new song to the Lord. More than simply citing chapter and verse is involved here, though. The Biblical principle is that of the Davidic liturgical revolution, where David took the dust-gathering Levitical traditions and started improvising. Peter Leithart in From Silence to Song points out that David seemed to herald in a special liturgical period, where he and the musicians could worship with the Ark of the Covenant face to face. If the Davidic liturgical revolution took place under these circumstances, how much more should music be jubilant, noisy, and, above all, new now that the veil has been torn?
2. Church music must be complex. The voice of the Church past speaks out strongly against this one. That's not an infallible argument, but nonetheless one difficult to reckon with. There is nothing complex about Gregorian chant or a Lutheran or Calvinist hymn or Anglican chant. If you're calling yourself a traditionalist, this is probably not the argument you want to employ. It's also important to remember that contemporary music is difficult for many people to sing along with for a reason—the rhythm tends to be devilishly hard. None of this is to say that Church music can't be complex. The really complex thing here is the issue, not the music.
3. Church music must be Classical. Sed contra. This is one I particularly take issue with. I would say the opposite—Church music needs to be not Classical. Remember what Classical means. Classical doesn't just connote "older", like classic rock connotes Led Zepplin (old, ha, ha, ha), but it also connotes the real Classical era, the era of Aeschylus, Sophocles, and Euripides. It's no coincidence that these men are one of the first recorded instances of art for art's sake and the use of the stage rather than the altar or the hearth as the background for music. Nor is it a coincidence that the movement that molded the direction Classical music would go was a group of Renaissance men who thought music needed to be less sacred and more like, of all things, the era of Classical drama. More about that here.
Think about it this way. If you have a problem with taking the devil-worship words out of a metal song and putting in great theology, then you should also consider there's a similar (maybe not so drastic) problem with Mozart's Requiem. Think about it—the same compositional techniques Mozart used for his definitively secular symphony he is now using for his ostensibly sacred requiem. If you think that simply slipping in good theology (well, even that's debatable) on top of secular music is in general a bad principle, then Classical music is precisely what you don't want your Church music to be.
This also gets into how you define Classical music, of course, but I think it's vital to understand it as a secular project, not a sacred one. So, this ends up going both ways—music that is truly sacred can't be considered Classical music. This isn't just an arbitrarily subversive category. Church music does need to be culture defining, not culture defined. It necessitates careful distinctions, and the clearest one is between High music that is sacred and High music that is secular. If this involves declaring that BWV 244 is not Classical music in the normal sense, oh well. It's a distinction that still needs to be made.
I'd also like to address, at some point, the concept of music as a mood enhancer. This should be enough for now.