It doesn't affect your friendship levels but it won't make them change into their original shirts. They just change into a plain white one. I think it only works if they're wearing pattern designs and not the clothing that is included in the game.
I like to change my villager's clothing a lot so there are a few different methods I use.
If you don't mind them displaying shirts in their house, just send them two or more letters at the same time, with the shirt you want them to wear attached to the letters. I think they like it more if you gift wrap the shirts and if you use a bunch of symbols (like stars and stuff) in your letter, so that might make them more likely to wear it.
If you don't want them to display a lot of shirts in their houses, there are a few alternatives. You can fill your pockets with items they won't try to buy from you, like flowers, and put the shirt you want that villager to wear in one of the slots. Save your game and go talk to that villager a few times. If they don't offer to buy or trade the shirt from you, go do something else for a bit. If you've done something important in that time, save your game again so you won't lose your progress. Then talk to that villager again. Keep doing that until they try to get the shirt from you. When they do, they should change into it. If they don't, quit without saving and try again. You can use something like the PWP trick to speed it up, just go into the sea and stay there for at least five minutes, then go back into your town and make sure that villager is the first one you see. They'll ping you and it might be about buying the shirt. Give it to them and quit without saving if they don't wear it.
You can also write a letter and attach the shirt to it. Shortly before a mail round (there's one at 9 AM and another at 5 PM) save your game and mail the letter. Wait for a while until it's a few minutes after the mail round hour and go find that villager. If they're not wearing the shirt, quit without saving and try again.
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By the way, if you put up designs you've made in the Able Sisters shop, villagers are more likely to wear them. You could try that if you're getting an epidemic of ugly shirts.
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I'm fairly certain that Isabelle can only change catchphrases, like if you got them from someone and you found that their catchphrase was offensive she can change that. I think they will only change their shirt if it was a design. Not 100% on that, but I do know that it will not effect friendship levels at all. She's there because of the real world trading aspect and they want to protect little kids who play the game.
That's not true. Isabelle can also change clothing and letters.
