I haven't seen this option mentioned yet but you can also order your groceries online, and have them delivered. That's what I do at the moment, because I live outside the city and my nearest grocery store is 2 km away. I could bike or hop on a bus, and I do sometimes, but ordering online is just really convenient.

If anything it's the car-dependent infrastructure that is ableist, as many people with disabilities cannot drive. I can't, and if I didn't live in a place where alternative modes of transport were a thing, I would either be stuck at home, or have to waste money on buying a specially made car.

Far from all disabled people use wheelchairs or have mobility issues. Some have problems with their sight, concentration, fine motor skills etc. which prevent them from driving safely. Even if you cannot walk or ride a bike, and have trouble getting on/off public transport by yourself, living in an environment that is walkable and bikeable usually means that it is also easier/safer to get around in a wheelchair or on a moped.

I've heard that you fall off the edge of the world, if you go too far.

People here are not for completely banning all cars, but for reducing the use of private cars. I personally don't think personal cars have a place in society (outside a couple of edge cases) and that we should start phasing them out. Other people just want better alternatives. I don't think I've ever seen anyone argue that disabled people, who need a car to get around should not be allowed to have one, or that we should ban taxis and moving companies from using cars.

I think that would be a very difficult trip to make without a car, but you could easily make that trip without a private car, especially in a society where that is the norm. You could either rent a car for a day or two, or use some kind of moving/transport/taxi service to get around.

Another perspective is that society would look different if is wasn't the norm to use cars to get around, and maybe you wouldn't need to travel as far to get to your local shows. I know nothing about showing dogs but I've grown up with ponies in my backyard, and from my childhood home (in the middle of nowhere by Danish standards) I could walk to a couple of horse camps and shows per year. Within an hours drive there was plenty to do, every weekend. We just kept our ponies as pets/lawn movers and took them camping or to a 4H show once in a while, and we rarely needed a trailer or even a car for that. When we did need a trailer, we would rent one at the local gas station or hitch a ride with someone.