Here are options I can think of:
1. Your users can make google accounts connected to their non-google email addresses. Google will let you sign up for a gmail account named "_
exam...@outlook.com" (or at least they used to).
2. Instead of using Google accounts for OAuth, you could do OAuth from Microsoft or Github or Trello. You should be able to support multiple different providers at the same time, like if some of your users have Google accounts and the others have Microsoft accounts. This option would require some changes to `pheweb/server/auth.py`. I can give you advice on those changes if you need it. I'd like to have this change integrated back into the PheWeb sourcecode.
3. You could hard-code a list of usernames and passwords. Then you could either use Basic Auth (by just giving a htpassword file to Apache or Nginx) or you could make your own login page in PheWeb (which also sounds quite do-able though I wouldn't help much).
Peter