I know where you're coming from, OP. My mother was very much of the idea that if she wanted us to help with chores, then she wanted it doing now, no matter if I was in the middle of a Latin translation or something.
I don't have any issue with the idea of having to do my share of chores (well, if I am honest, I did have some issue with it, and now I live in my own house, my vacuuming and dusting doesn't get done as often as my mother would have approved of, because what's the point, if you aren't actually going to see any difference?) But I did have a problem that I had to do it right now, and even 25 years on, I feel myself getting a little wound up that she would never negotiate - there was never any acceptance that it would be okay to do it in half an hour when I'd have finished what I was in the middle of, or anything like that. If I had then not started in half an hour when I'd said, then it would have been fair enough to have a go at me, but ... oh, let's just say my mother was bloody unreasonable at times, chores being the least of it. I don't think I ever argued about stuff that really did have to be done right now, like rushing to get the washing off the line because it was starting to rain, because I knew that really did need to be done right now.
I think that learning to negotiate and prioritise is as important a skill as learning that you have to take part in household chores when you are living in a house. So go and talk to your mother as someone else has suggested, and say that you agree you have to do your fair share, but you'd like to talk about timings and interruptions. And whatever you agree to, make sure you keep your side of the bargain, and if for some reason it's not working, then don't just stop doing stuff, but have another discussion about how things could be changed.
(Unloading a dishwasher isn't a big chore, though. Be glad you don't have to do the actual washing up.)