Your horse is absolutely gorgeous! I agree with everyone. No one knows your horse like you do. Some horses adapt very well to having one eye and go on to have very successful careers. Bishop looks like he's very happy, keep it up!
If you see the bay horse in my advatar, he is blind in one eye as well, but you can't tell since he physically has both his eyes.
With my old horse Mikey, being blind in one eye didn't affect him at all!
We showed and showed and showed and he loved it all up untill his death.
But, I do think it really depends on how your horse handles his handicap.
I do not think it is cruel at all!
If he is willing to do what is asked, then don't hold back!
Seems to me that your horse loves doing what he does.
Of course If he hesitant, then be cautious and don't push him too much
He's about 20 -21 now, Im not 100%. That's why I want to slowly retire him, because he may be older then I thought, and I don't want to ride him hard.
He's a total schoolmaster, he is the horse my friend learnt to jump on. He's a bit lazy lol, but he does fine. I make sure to never jump him higher than 70cm, because he has a funny jump. Sometimes, he only lifts his hind legs, when his front legs are all ready over lol.
My daughter has a 20 yr old mare that she does barrels and pole bending on. This mare has had her right eye missing for at least 10 years or more. When she rides her into the arena, people snicker and laugh, then when she finishes her barrel or pole runs, everyone jaws drop. This mare is FAST and she can do the poles and barrels without a mistep, even the right hand turns. She has run high 18's on a big pattern and low 20's on regulation poles. Not bad for a one eyed horse.
Your horse will tell you what it can and can't do