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)

Just use:

    'http://id.fedoraproject.org/'

Instead of:

    'http://{0}.id.fedoraproject.org/'.format(fasusername)

[coprs_frontend/coprs/views/misc.py]

And check for allowed usernames later, after you get the username from FAS.