Maybe there is some interference from some script. Try turning them off to see if the bug disappears. If so then turn them on one by one and check if the bug reappears. You will find out which one is the culprit.
I think in the end for them it was an issue with antivirus software that was causing the issue. Maybe check that out or try clearing any cookies that you have installed. Have you also tried WaniKani in a different web browser?
Thanks @DollyDaydream, this sounds identical to the issue I was having, which turned out to be due to Kaspersky’s free security cloud (I’m not sure if this applies to other AVs). It might have been possible to solve the issue by tweaking the settings since I’m guessing that it was something to do with the active monitoring by security cloud in the web browser which probably could be selectively switched off somehow, but I just ended up uninstalling it (which solved the issue).