I had the same problem when I first agreed to the new license but quit the application before login. In the application support folder (~/Library/Application Support/SourceTree) there was a json file named "20160217_<some uuid>.json" containing something between 5 and 6kb of binary data.
I renamed the file and restarted the application and the login page was visible again. I am not sure whether there is any relationship between this file and the login page. Maybe pure coincidence... But after that a was able to login and use sourcetree again normally.
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