How do you deal with over-competitive riders?
Ignoring them would be best. However, that's not other possible. You are after all on a horse that's going to know if you're simply pretending they don't exist while being silently bothered. I'm almost positive that horses hate a rider who's lying to themselves or pretending than a rider who is scared/bothered and does not attempt to hide it.
Depending on what your horse is close to, you may have to avoid. Horses are amazingly sensitive and can pick up feels. A feel is resembling an aura only less New Age. It's like how you know when your mom is contained by a bad mood and that you shouldn't ask her about buying you something.
If you or your horse can't stand the feel of the super competitive family, you should probably avoid them. If you can really ignore them then it might not be a problem. Just tell your horse that "That is not my ride" and don't pick up the get the impression of the other riders. It's harder than it sounds.
You can always console yourself by thinking that they're going to get in a valid wreck eventually. Unless they're actually good and not piss off the horse.
But perchance you should get to know more people who aren't competitive. Like a bunch of friends who just ride for fun.
merely ignore them if they are rude to you.
take no notice of them .