Very far removed. Not even the same issue. Bows are completely optional and just a fashion trend.
Naturally voluminous, curly hair is simply how some peoples’ hair texture IS. There are, yes, different protective styles that can be done, or sure, they can straighten it (which, how damaging can straightening one’s hair be depending on the method used? Straightening hair usually uses at the very least heat and in cases of incredibly curly hair, chemicals, if I’m not wrong.)
This isn’t even the same issue. And personally I’d say that if that person wants to compete they need to follow the rules outlined by their discipline’s governing bodies, in this case, assuming the dressage rider is an American, that would be the USDF and/or the FEI.
But again, not the same issue, at all. This is an issue where a large group of equestrians with a specific natural hair texture cannot find a basic piece of safety equipment that is often required at most barns and competition venues, to accommodate their natural hair texture. One shouldn’t have to use heat or chemicals to temporarily straighten one’s hair just to participate in a sport. Especially given one is usually expected to wear a helmet every time they’re riding - if someone is riding 4-5 days a week, well, they’re pretty much going to have to keep that hair straightened via potentially damaging processes, indefinitely.