Paying to have my home cleaned feels uncomfortable because it's something I could do myself, so it makes it very obvious that my time is being valued more by society than the cleaner's.
I generally find people who work for cash, and we negotiate fair prices.
I don't think that works as an explanation. I have no compunction about buying hot food even though I can cook myself, and I'm sure I could easily have learned to repair a couple of things I paid to have repaired for me.
In most service industries, you have people serving many different customers at once in a way that's usually more efficient than every individual doing the work. But if I pay for a cleaner, I'm paying someone to spend time doing almost exactly what I would do otherwise. They're probably slightly faster than I would be, but otherwise there are no economies of scale obscuring the inequality, and that's what makes a lot of people uncomfortable with it.