After the ad blocking is turned on, many normal functions of the website are filtered, and the website cannot be displayed normally.

On normal websites this usually does not happen. Sites, who use suspicious tactics (like binding some key functionality to google scripts or similar) can be affected; you can disable adblocker (or part of it - privacy blocker) for such sites. I prefer to find alternative sites then, of course this is not always possible.

Care to share a link to affected site?