We have a cleaner who comes once a week, I usually do a tidy up the night before (I find its a good prompt) as like others, I want her to clean - not tidy
We have agreed that she will place any items that she's not sure about in a a designated washing basket - but as she's been working for us for over three years that's pretty rare.
I know with other clients she does absolutely everything, dishes, laundry, trash removal, ironing etc - but that's not the arrangement we have. I think an effective cleaning service understands the needs of each client and works to meet those, understanding that different clients will have different needs and priorities.
Sure - if there is a health risk or the cleaner in uncomfortable touching certain items (breakables etc, or I know my parents cleaner refuses to dust the wine rack/cellar as she is afraid of disturbing it) then they bring that up in a diplomatic fashion, but I really don't see how stuff on the kitchen table prevents a cleaner from doing the bathroom.
I think the OP did the right thing in ending her association with this new cleaner, clearly it was not going to be beneficial