CNN is an overly elaborate site, with many simultaneous videos playing, lots of ads (some of which are also videos), and for me (I don't log in on CNN) using an older Macbook Pro 16" 2019 (Intel), at times the site is downright sluggish. That said, the site does work for me. I have a fairly vanilla Mac setup. I suggest you carefully go through all the Safari (or whatever browser you are using) settings and preferences. Safari allows users to set individual settings for specific web sites. Also, look over any browser extensions installed, maybe trying uninstalling all of them to try to remove possible causes.
Trying different browsers might shed some light. Which browser are you using?
If your Mac has any network security tools, VPN, network monitors, "cleaning software," or anti-virus, as a troubleshooting step I would uninstall (not just disable) them all. (They can always be reinstalled, although I would not recommend using any of those types of tools).