Not sure why anyone would say it’s best to keep a bunny outdoors. o.O Did they give you reasons?
Inside they can be part of the family, sleep in the bed if they learn to behave/want to (some can, some can’t), have run of the house (once they are trained well enough), get constant attention, etc. My buns sleep at my feet, one used to sleep in my bed and they are more like cats than anything. They come to me when they want attention, they let me know when the food is empty, they just hang out all the time I am home.
Outside, they only get attention when you have the time to devote to JUST them (instead of curling up on the couch to watch a movie with the bun beside you), are vulnerable to fly strike, predators (a cat, dog, hawk, fox, rats, ferrets, possum, etc etc), diseases from outdoor animals (mice, spiders, snakes, wild birds, etc), parasites from the dirt/other animals feces, weather. Plus, if there are any weeds/plants/flowers that are toxic to them, it’s deadly. And if they get sick (gas, GI stasis, tooth issues, various other common health issues) you are less likely to see it if they are outside vs inside where you can pretty much always see them. My two have had tummy issues twice, both late at night before bed and both required attention to avoid becoming full on stasis… if they had been outside, I wouldn’t even have noticed until the next morning since I would have gone to bed instead of walking by and noticing the loafing and uncomfortable looking rabbit.
For allergy control – you can get an air purifier to keep the hay particles out of the air some. Daily vacuuming can help. Wash your hands after handling bunny or hay. If you keep any food inside, you can store it in a plastic container so it is contained a bit.