From the animated gifs it looks like you're just presenting an Anki deck online. Why not just share what you have to share as an Anki deck?
Why not just save progress as a cookie? (Why do websites have to have centralised corporate surveillance?)
I don't want to continue where I left off on another machine — right now I just want to see the thing in the first place.
If you expect people to sign in before they can see your content, presumably you expect they already know that they want your content — enough to overcome the hurdle of giving access to the 3rd-party account that you assume they already have or are willing to create.
Progressive enhancement!
i also had a lengthy constructive exchange with the person handling the case about the downside of this policy and why one might legitimately want multiple github accounts.
the response i got suggested that if someone could bring a legitimate case why they needed multiple unpaid accounts, then they would be willing to make an exception. which means, at least they are willing to listen to reason.
personally, i think that if you use github for work, then it's a fair argument to say that that should be a paid account.