I hate to be the bearer of bad news, but we also had this problem, which flagged on the Facebook Dev page: https://developers.facebook.com/support/bugs/406930029718049/
They have looked into the problem, as a number of us have had this exact issue too. It is only affecting EU user, as our US users are logging in and signing up without problems, and it seems that Facebook are refusing to look into it - their Instagram Platform API forum has already stopped accepting issues.
In terms of what we have learnt since last week, we think:
UPDATE:
So it seem's it is in fact a cookie issue on mobile. When a user goes to sign in on mobile view, the 'accept cookie' message that typically appears on web doesn't appear. However, when the error screen pops up, if you click 'Log in' in the top right, it will redirect you to the web view, which lets you accept the new terms and conditions. Then, once you direct back to mobile the cookie seems to have been saved and you can now login. This has worked for us on iOS so far, but not Android, and we still haven't come up with a work-around yet.