Try hitting https://old.reddit.com/ in an incognito window. I've been faced with this at least a week now. I just stopped reading subreddit content tho. I'm not creating an account, and new reddit is pretty awful.
Wouldn’t work for me for about a couple weeks so I just stopped using reddit. Worked today when I tried again. I always use private tabs because I don’t like cookies/tracking across sites.
Still works for me, even in incognito. Also, I've never had a Reddit account, so there's no chance of some sneaky automatic login or something.
Someone a little while ago suggested that perhaps they're incrementally rolling this change out or something, and it just hasn't hit my part of the US yet.