Essentially a user offers to share their calendar with another, and also checks to box to request access to the receivers mailbox. When the receiver gets the mail and clicks "Allow" Outlook locks up stops responding. You have to either wait for Windows to kill the process or do it yourself in the task manager. Has happened to all users that I've tested it on now.
I posted this originally in the Exchange forum by recommendations of someone, the Exchange forum told me to come here.
It happens in Safe mode as well as normal instances of Outlook. It doesn't appear to cause any issues in the OWA though, so that's at least a small workaround I can provide my users.