How can I stop the persistent pop-up window of the Screen Time popup window?

I've configured my Screen Time settings under Content & Privacy > Content Restriction to block certain domain names and IPs for privacy and to prevent web trackers. However, whenever I use a browser other than Safari, persistent pop-up windows hinder my browsing experience. These pop-ups demand constant acknowledgment, rendering it impossible to perform any tasks. Is there a solution to prevent these pop-ups without being limited to Safari? My work requires the use of more than three browsers simultaneously, and some essential extensions are not compatible with Safari. Suggestions to exclusively use Safari won't address my needs. The main concern is how to halt these intrusive pop-ups across various browsers. I want to prevent specific sites, like Facebook services, from establishing connections with my computer. For example, every time I encounter a login page offering options to sign in with Google, Apple, or Facebook, an obstructive window appears, disrupting my workflow on my MacBook.