I have to agree with iride, DO NOT SLOUCH! You still maintain a good posture when you're riding western. Your back should be straight, shoulders relaxed. If somebody were looking at you from the ground, they should be able to draw a line from your ear to your hip to your heel. You can't get that if you're slouching!
I don't know WHERE anybody learned that you can slouch in a western saddle, but it's simply not true. I have been riding western for around 18 years and have studied with many different trainers in pleasure, gaming, reining and the like. I can also ride english as well. While it is slightly different than riding english, your posture need not go out the window!!