I've got pretty strong feelings about how far I'll go to make my horse "presentable" for a show. I'll shave the outer edges of his ears, but leave the inner hair. I leave the whiskers on his muzzle and eyes alone. I don't pull his main, and I don't pull tail hairs. His mane helps keep the flies off his neck. I don't even mind letting him bleach in the summer because, as a black horse, fading to a dark brown probably helps him stay cooler in the sun.
If my horse were stalled at least 20 hours a day, as many show horses are, these things wouldn't be such an issue. But my horse is out to pasture most of the time (I wouldn't have it any other way), and I want him to be as natural as possible.
So, I think that a horse should be able to go into any show ring with a running braid. Why should a horse have to have it's mane chopped off or pulled just to be competitive if there is a reasonable alternative such as a braid? I don't have anything against a horse having its mane pulled--it's just not appropriate for my horse and the conditions he lives in. JMO