Compare tables always keeps products

As the author explains in this topic here: https://www.ads-software.com/support/topic/impossible-to-leave-it-empty/ . It is impossible to keep the compare tables without items if you are logged in. Adding items to compare and deleting them with logged in account are appearing again on the next login.

I try to deactivate all the plugins, change theme, and so on. Nothing helps.

Any idea what can cause this problem?