No it's not rude to speak up at the salon. It's your hair, it's your money, it's your appearance.
So what if they went to school for what they're doing. Maybe the curriculum at the school needs to be revised if they're not being taught to comb from the ends up, be gentle with hair while washing, don't apply relaxer to the scalp, etc.
I haven't been to a salon in 4 years but I did offend a stylist by speaking up. I had gone to that stylist every 2 weeks for years. I had started taking better care of my ends and I started saying "I don't want a trim this time" when I got a relaxer. The more I did that the more upset she got. The last straw was when she said "you know when you don't get a trim I have to cut off more the next time".
After that I found a new salon - a Dominican salon. They did what I wanted.
It's fine to speak up to anyone who went to school for what they're doing - a stylist, a nurse, a doctor, a lawyer, a teacher, whatever.