Training and testing image sizes for classification in computer vision
It's important that all of the training and test images have the same aspect ratio but it doesn't necessarily have to be the natural one. If you think about it for a while you can see why that is. For example, if you're making a face detector and you have altered the aspect ratio to make all the faces look abnormally tall and skinny then you have a tall and skinny face detector. It won't work unless you do the same transform on the input images.

I'm not sure if I believe you about opencv making all the inputs to the cascade classifiers square. There is no reason it has to be square as long as all of the training images are the same size.