I'm not saying cropping is wrong or taboo, I know it's done quite often. Just not by me. I'm with Nathan on this. Looking at a square and planning rectangle just doesn't feel right to me. I'm sure that I'm being nonsensical and irrational here, but I'm only human.
I would never dismiss a photograph because it's been cropped, I just don't prefer to do it myself is all.
You are perfectly normal. A lot of people feel the same way as you.
This actually makes it easy. Do you prefer your final image to be square or rectangular? Buy a camera that fits your preference.