Description of problem:
When I log into Copr, I have to put in my username only to be prompted again on FAS side.
This is indeed not needed. For example see FedoraHosted OpenID login link
https://fedorahosted.org/copr/openidlogin (see source)
And check for allowed usernames later, after you get the username from FAS.
Fixed in upstream in commit 1958ff0