Chrome Extension: declarativeNetRequest to bypass Content Security Policy breaks web application which makes XSS calls to other URL or service

Question

I have developed an extension with v3 manifest to execute user script in my extension, I followed steps suggested by wOxxOm in Chrome Extension: How do I inject a script that the user provided? & then to overcome "Refused to execute inline script" error, I used declarativeNetRequest to bypass Content Security Policy (Chrome Extension: How do I use declarativeNetRequest to bypass the Content Security Policy), but that breaks many websites (whichever try to load some resource from other origin and have strict-origin-when-cross-origin policy) even when this extension is just enabled. is there any other alternative which we can use to overcome "Refused to execute inline script" error and without compromising Chrome security & Website behaviour?