Circumventing third-party request blocking in extensions

[notrms]

Hi, and sorry if this is a question that could be solved with some 
simple searching!

I'm developing an extension that loads the otherwise JS-dependent media 
files on certain websites, and run into issues with third-party request 
blocking blocking third-party requests. Setting the "src" attribute of 
the appropriate tags does nothing, and making an AJAX request from a 
content script is just as successful. Interestingly enough, Tor Browser 
does allow the requests (not that many people would install extensions 
in it).

Is there any way to load the resources, other than disabling blocking? I 
can understand if there are some ethical issues, but if the user 
installs the extension that would seem to be implied consent for it to 
conduct its stated purpose and what that entails.

Thanks,
notrms/jahoti