Horse manure does carry parasites and other nasties but most are not transmittable to people. So this is not a big concern. Of the ones that can affect people, they do not have the same effects as they do in horses. You might see some skin irritation but you won't normally see parasitic remains in stool, etc.
I do have a better solution for you though. Some of the larger feed stores will pick up your discarded manure and give you a small credit towards a feed purchase. I know that Southern States in our area does it.
I would approach the stable owner more from an economical standpoint that a health standpoint. You have to make it better for him NOT to put it where he's putting it.
Gardeners and nurseries can always use manure so this is another alternative.
Does this help? If not, let me know and I'll try to come up with more.