Such websites make use of different anti-adblock services or use their own tools to make you disable your content blocker. As soon as they detect a content blocker, they show a pop-up asking to turn it off.
Apple's native content blocking API is quite limited at the time. While some pop-ups are easy to block, others contain random names or use tricky timers. It is hard to protect you against such pop-ups, using the current toolset. However, we hope that Apple will provide us with a tool that would allow us to remove such elements in the future.
The good news is that we still have options!
For instance, lots of anti-adblock notifications are successfully removed by built-in filter rules. Also, if you are familiar with CSS selectors, you can try hiding them creating custom rules in the "Hide element" category.
Sometimes it is worth whitelisting the site or reloading the page with content blockers temporary disabled (learn more: Quick Access to Content Blockers in Safari). For example, if a pop-up is not covered by the current set of rules, and you need to have access to the website under the pop-up.