I also had the Fastmail problem — after entering my credentials, the loading wheel would infinitely spin and I couldn't get to my inbox.
Inspect Element > Storage > Delete Cookies and Local Storage also worked as a fix for me, with a caveat. When I logged in with "Stay signed in to Fastmail" checked, this fix didn't work — it still resulted in the infinite loading page. When I cleared my cookies and storage again, and logged in without selecting "Stay signed in", the Fastmail inbox loaded right away!
On 0.99.120.1-beta