I don't consider TKD to be a sport, despite doing WTF (the Olympic style). As you said it depends on the instructor. In my regualr class we cover competition sparring, sure, but the main part of the lesson is based on techniques that you would use in the street, as it is after all a martial art, not martial sport. I'm so used to using take-downs, sweeps, holds and floor work that I assumed this was standard TKD.
Over the summer I went to train at a different club (as I normaly train at my university club). I found a WTF club thinking it would be similar. The instuctor is a 5th Dan, and there's no doubting he's earned his title at all. However, it became clear to me that none of these students had come close to do anything like a sweep, or kicks to the knees, or below the belt (apart from a front kick to the groin). From this experience I can see how it could be considered a sport, as most of the training we did (apart from 1 and 3 step) was concentrating on the best way to score points in a competition.
I think the attitude towards TKD depends on the instructor. As someone that hasn't been studying it for an amazing length of time, I can't say how much of what I'm being taught is "pure" TKD, but we're taught what we are because it's practicle.
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Have you ever entered any open competitions?
