If a web server has a CSP, Service Worker or crossorigin/integrity attributes, it may be possible that LocalCDN isn't allowed to replace anything.
Content Security Policy (CSP) is an added layer of security that helps to detect and mitigate certain types of attacks, including Cross Site Scripting (XSS) and data injection attacks. These attacks are used for everything from data theft to site defacement to distribution of malware.
https://developer.mozilla.org/en-US/docs/Web/HTTP/CSP
Service Workers essentially act as proxy servers between the website and you. It's possible that a Service Worker may deny replacements by LocalCDN. In this case, you can disable LocalCDN for this website or globally disable all ServiceWorkers:
https://www.ghacks.net/2016/03/02/manage-service-workers-in-firefox-and-chrome/
Crossorigin and integrity attributes prevent the replacement by LocalCDN. Enable the HTML filter to remove these attributes and allow LocalCDN to replace the framework. Please note that this may cause display errors and the HTML filter is only available for Firefox.
https://developer.mozilla.org/en-US/docs/Web/Security/Subresource_Integrity#subresource_integrity_with_the_script_element
