This question can be easily misunderstood.
People jump into the conclusion that Europeans stop people with a fake handbag over their shoulders, which is obviously preposterous. If you’re carrying a single replica bag, a wallet, scarves, or watch, absolutely no one will stop you at the airport and try to authenticate your items.
In a US airport, TSA doesn’t give a damn about the number of stitches or pattern alignment. I am convinced the middle-aged men wouldn’t recognize most of the brands as they have zero interest in fashion, and they are not professional authenticators.
Even though reps are technically illegal in the EU, if that item is clearly for your own use without any intention of making a profit, the authorities don’t bother.
A lot of people probably carry fakes without even knowing it and checking everyone would be impossible given the number of people at airports. If you’re walking through the customs after your arrival and you have an in your face large brand new orange LV shopping bag, they will stop you and ask you where you bought it and will want to see a proof of purchase, in hopes of making you pay the VAT in your country. This is not true if you buy something in the Schengen area and bring it to another Schengen country.
So if you purchase something abroad and you want to keep the box, just put it in your checked-in luggage and carry the item itself as your hand luggage.
If you just landed from China and your luggage contains 20 designer handbags worth 30k Euros that are the same style, the TSA people don’t have to be professional authenticators to understand that there’s something fishy will obviously seize it.
This is what it meant by saying it’s illegal to carry replicas and will most definitely get you into trouble.