As long as you have added a key to your account this is a bug, if you haven't added a key then you cannot play beta yet and this is the normal error. However if you did add a key already there is a couple of things you can try to fix this bug, it's semi common and these are the best fixes.
1. Make sure when you login to battle.net it is showing Hearthstone on the account list. If it isn't then you have not been added to the beta(or added your beta key) so you cannot play and will get the region error.
2. Change your password, this can make the account update and get it working again. (Most common working fix)
3. Uninstall Hearthstone and BDA, delete the cache folders https://eu.battle.net/support/en/article/deleting-the-battlenet-cache-folder-windows
Then reinstall BDA then HS making sure it is the US clients for both. Even setting the EU client to US won't work atm, it must be the US client if your account is US.
4. Make sure you are logging in to the right server, the beta is locked to your home location and you currently cannot play on the other servers.
5. Try 'resetting your region' by logging out of the battle.net app and changing your login region to US or Asia, then login, logout and relog back into your normal region.
Twitter: @Narull | ANZ Diablo III MVP
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