I believe they're looking into the issue to find the cause but in the meantime, you should try removing and re-adding Real ID to your Battle.net account. You can do this yourself from your Battle.net Account Management page as long as parental controls are not enabled on the account, otherwise, it will require the parent to do it instead.
On the Main Battle.net Account Management page, select:
Account > Settings > Communication Preferences > Privacy
I suggest changing the account password before re-adding Real ID as that will force a refresh of the account data.
This has been fixing the freezing for nearly everyone trying it so give it a shot if you're having this issue.
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