I would discuss this with the pediatrician, the school nurse and maybe the teacher. If there is an odor around her, they can get involved and explain that it is noticeable. Also, they are not her parents so, frankly, their opinion carries weight! Also, if she goes in to the doctor for a checkup with stains or an odor, the doctor can address it right there, without it having come "from you." Obviously, alert the doctor or nurse ahead of time, but let the comments come from them. Your daughter will start to lose friends if she has an unpleasant odor in school. THAT might make more of a difference than "Mom doesn't like this" or "It's unhealthy to be covered in bacteria-filled poop."
It's also important to find out - in a quiet time - WHY she doesn't wipe. Is the toilet paper too rough? Is it hard to figure out exactly WHERE to wipe? Does it feel invasive to clean up inside the crevices of her body? Does she avoid the possibility of her hands touching poop or pee through wet toilet paper? It sounds like you've tried the thicker wipes which are not likely to shred or get a hole, but maybe she needs reassurance in this area. Once you get some answers, it will help you know where to focus.
I would not humiliate her, but I think you can take concrete steps to make it more of a hassle to clean up afterwards than it would be to wipe. If doing laundry and cleaning stained underwear is more difficult than wiping, she might shift her behavior. Do it matter-of-factly, that this is what is done when clothes are stained, particularly with body fluids. This is important for everyone to realize, but especially girls who will get their periods one of these days. If she starts hiding her underwear in her drawers or elsewhere, then EVERYTHING has to be washed, dried and folded. If she hides it in the bed, then she has to wash the sheets. She can't go out and play until the chores are done. If she has an allowance or money from Grandma, then it can go to pay for all the extra detergent and stain remover. Simple economics - YOU pay for normal laundry or true accidents (like spaghetti sauce on the shirt - but SHE pays for avoidable stuff that comes through her own behavior.
You could also consider putting a feminine pad inside her underwear to protect the clothing? It might keep things from penetrating her underwear, but also be uncomfortable enough - in a grown up way, rather than a diaper - that she doesn't want to deal with it every day. This can't be too punitive, because she will be getting her period one of these days and you don't want her hating products she will need at least a few days a month, but now she will need them all the time.