Topic on Extension talk:TemplateStyles

$wgTemplateStylesAllowedUrls will allow you to whitelist pre-approved resources. Just don't define more than one $wgTemplateStylesAllowedUrls array in LocalSettings.php, otherwise it confuses the software.

I have a local collection of commonly used images in the [wiki’s url]/common/images/ directory, and I wish to use them in a wiki via the background-image directive.

While I can easily do that on MediaWiki:Common.css, it takes about 605 lines (for 605 images) and I thought about putting it in a TemplateStyles Sanitised CSS, so that the rules only load when there is a need for it.

What do I need to do to whitelist the local repository?

See the docs for $wgTemplateStylesAllowedUrls in #Extension:TemplateStyles#Configuration.