You can still follow people! Well, sort of...
Thank MasterZsword for this info not me: "Technically, you still can. If you know their username or email, you can search them by clicking the search button where the leader board is. From there, it should give you an "add" option. Hope that helps!" Thanks again!
Hehe. The program I used to record the animated gif image is called GifCam. It is extremely simple to use, completely free, has no ads or any other rubbish, runs direct from its exe without needing to be installed, and takes up less than a couple of megabytes. Then I simply uploaded the gif to imgur and attached the image like normal. That gif in my post is only a mere 310 KB too. ^^
Major website updates. So, some features are winking on and off as they go about making changes to the code (or whatever they do to make stuff change). Also, they are collecting everyone's feedback and then making additional tweaks to stuff here and there. I'm sure that makes even more stuff bump around. This is pretty standard for huge updates from what I've seen over the last four years.
I don't have a list of what they are keeping and what they are removing. It's always best to be prepared though. So, since the follow button is winking on and off, if you have Duolingo friends and you are worried about the follow/following lists disappearing, I'd write down your friends' usernames or take a screenshot of your follow list and save it just in case. :)