This confused the fuck out of me until I realized that Mastodon instances have the option for users to allow or deny follow requests. Basically, if you click on someone's follow and nothing happens (or you get an error page), what's happened is that you've sent them a follow request that they have to approve. Kbin's interface fails here (hopefully will improve with update) and does nothing. If they do chose to let you follow them, you'll see their account update.
God this explains so much. I tried hitting the Follow button multiple times in a row and now I probably look like a crazy person spamming someone with follow requests. ;_;