This manga has two aspects. The first aspect is instructional guides on how to clean various things in a normal household. This is probably the original hook the rest was built around, but it wasn't executed very smoothly. In order to justify the extensive cleaning necessary for this type of educational shtick, they had to create a convoluted scenario involving multiple instances of child abandonment. And they ended up dropping this aspect halfway through.
The second aspect is a clash of values. Character A makes decisions based on duty--on feir duty to others as well as feir duty to femself. Fe is flung into the life of Character B, who has little to no sense of duty. Fe doesn't even feel a duty to femself, to keep feir home clean. Character A resents fem and sees fem as a selfish and entitled slob. But then while cleaning feir room ('cause fe feels duty-bound to help feir clean), fe finds evidence that Character B too has a sense of duty even if it differs from feirs. And feels fe may be alright after all. Yea, it's pretty condescending.
The moral of the story is that you should live with a strong sense of duty because those around you will respect your earnestness, and it may even lead to sexually enticing girls wanting to embrace you. Honoring duty leads to booty!