I am guessing you are in the protestant wing of the church which seems to have two strands to it: there IS an iconoclastic tradition in the protestant church which winds its way through Calvin and the Puritans (in UK of course it was Cromwell and co who put an end to the great Elizabethan artistic flourishing) but Luther is always absolutely clear about this, and it was Luther's theology which sparked off the amazing torrent of perfect music in Germany after the Reformation. I think its not too simplistic to say: 'no Luther: no Bach'.
I spent many years teaching music in a Lutheran country and their view of music is so entirely different to ours (which is more a sort of impatient tolerance or a vaguely sympathetic scepticism)that I was quite blown away, and profoundly inspired. It lead, when I think of it, to an artistic revival of my own. They placed music, quite instinctively, very close to the sacred. This view is shared by the abbot of a monastery that I visited many times (and was anxious to join, although my conviction has prevented it). For him there is no rift and he struggled to understand when I tried to explain my own dilemma. His view is also shared by Rowan Williams the Anglican Archbishop of Canterbury, who has written extensively and very beautifully on the subject. There is an excellent criticism here of the wonderful book by Williams called 'Grace and Necessity': http://anglicansonline.org/resources/essays/whalon/GraceNecessityReview.html

The Catholic church is almost as divided on the issue as the protestant one but, because of the more rigorous control, it tends to result in a gentle swing between the two poles from pope to pope. John-Paul II, for example, despite being a playwright himself, put out a rule which forbade the performance of secular music in churches (the Polish tradition is surprisingly puritanical)whilst the German Benedict, soaked in his own country's Lutheran tradition, often invites musicians into the Vatican to perform and has a view much closer to my abbot's, although there is always a niggling worry I have whenever I hear him speak about music (or about anything for that matter).
Rowan Williams actually cites the Catholic philosopher Maritain, who follows the Thomist view (Williams is definitely a Thomist) which is instinctively for me the 'right' one even when intellectually I feel barriers. Do read the article above, and if you can find a copy of William's book I can recommend it. It is breathtaking stuff for any Christian struggling with his art although Williams is something of an intellectual in the way he puts things.
I should point out that, from what I can see, the Catholic Church in America has soaked up far more of the Polish iconoclasm than it has the German Lutheranism and that the American Christian artist is therefore likely to be at a distinct disadvantage culturally. In America, as in Britain, art has been mostly 'hi-jacked' by the secularists, and it is a difficult and stifling place for the Christian artist to be. It is important for Christian artists to find each other so that they can breathe and talk together and throw off shackles that can trap and kill us without us even being aware of them.
I just want to close by pointing out the important connection between the view we take as Christians over the last supper and the eucharist in all this: the Real Presence versus the memorial. I struggle to put this into words not being a philosopher but Maritain puts such emphasis on the idea of 'art being more than it is' - which is a concept which doesnt really seem to mean that much until you put it up against the bread and wine at the Anglican communion service or the Catholic mass and realise how this bread and wine is 'becoming more than it is' in a miraculous way. This is an experience that you might understand from what happens to you when you listen to music rather less than from your understanding of the eucharist which may well be more memorial than mass I dont know. This awareness of the 'divine presence' in the bread and wine when all the priest has done is say a few half-considered words does link dramatically with what the artist is trying to do when he daubs a canvas with paint or splatters manuscript paper with crotchets and quavers and it links back for me into the gospel where Jesus surely teaches again and again that God is not just imminent but overflowing; irrepressible in his desire to reach out to us. . . . .my point being that music or an artistic experience of any sort, just like the eucharist, is ultimately a matter of faith and trust . . .
mmmm I have a feeling that I am writing this more for me than for you, but no harm in that I guess!
PS at the risk of overkill, it was occurring to me as I previewed this that iconoclasm is perhaps more of a central issue in the world today than is first apparent, because it is such an important aspect of the 'battle' between Islam and Christianity. The Jews also have always been iconoclastic,(until they became soaked in the Lutheran German tradition: hence Mendelsohnn and Mahler) and it did occur to me that Cromwell's puritan tolerance of the Jews (he invited them back to England) was based partly on the increased importance which the puritans placed upon the Old Testament 'way of thinking' which is highly iconoclastic: art being allied almost entirely with idolatry. (graven images etc.)
When we visit our churches in Britain we still see this around us: niches which had contained statues of the saints and apostles now empty and battered by Cromwell's soldiers . . . .
I am presently reading a book about the early church and the problem between east and west down through the centuries has grumbled on mostly around the fundamental difference in view between the iconoclastic east and the art-loving west . . . . . down until the present day I suppose . . .how this is directly relevant to us I am not quite sure!