"Your browser is not currently supported."

Just stumbled into this after I was unable to claim twitch drop for hours on end, nothing worked, not single browser works, removal of cookies/cache doesn't work, disabling browser extensions doesn't help either.

But I managed to bypass this in sheer luck, what I did was go to my mail and find "reset password" link under "Your Twitch Account - Successful Log-in" mail and it redirected me right to Two-Factor Authentication link, thas how I logged in. Posting this in hope to help someone.

Nothing did work that can be find on forums, and I can imagine you can basically be stuck forever in this loop, props to twitch for making it one of the worst experiences possible.