You can send a Mew to Pokémon Sword and Shield with a NEW Poké Ball Plus
The Pokémon Company has just announced that players who purchase a brand new Poké Ball Plus controller and use it with Pokémon Sword and Shield, they will be able to transfer the Mew inside of it into their games.
This, of course, requires players to have a new Poké Ball Plus though, meaning if players purchased the controller when the Let's Go games came out and transferred it to those games, they won't be able to transfer the Mew to Sword and Shield.
Serebii Update: If you connect a new Poké Ball Plus with Pokémon Sword & Shield, you can send the Mythical Pokémon, Mew to Sword & Shield
— Serebii.net (@SerebiiNet) June 11, 2019
Of course, you can always transfer the Mew through Pokémon HOME, the new Pokémon Bank, between games but it still is painful that you have to do this in the first place.
You might have also sold your Pokémon Let's Go games with the Mew trapped on your system and will be forced to repurchase the game to get the Mew you are craving. It also means that a lot of people might purchase a second-hand Poké Ball Plus not knowing the Mew inside is gone, disappointing kids everywhere.
Not that there is anything that we can do about it, but just be sure to save the Mew on your Poké Ball Plus device, if you have one available if you are desperate to get it into your Sword and Shield games.