just say no?
Don't tell the others that I do this, but when the animals are going to offer a shirt or piece of furniture I can easily get at the Nookling stores or Able Sisters in exchange for a rare fish I spent a while on getting, I say the common phrase using the f-word towards the game in a rejectful tone. If they can't pay me to take rare items like this, they're not gonna have my rare items.