From a discussion with @Nirmos regarding TemplateStyles adoption on Swedish Wikipedia
TemplateStyles (or perhaps more correctly css-sanitizer) does not allow protocol-relative URLs for background images and the like. It should.
When trying to use protocol relative URLS in TemplateStyles the user sees a message such as, "Invalid or unsupported value for property background at line x character y."
From @Nirmos, "Protocol-relative URLs are really common in the MediaWiki namespace, and there is a reason for that. In 2012, a global bot (ran by Hoo man) made all URLs in the MediaWiki namespace protocol-relative in preparation for the switch to HTTPS (which was made on June 12, 2015). https://sv.wikipedia.org/w/index.php?diff=15652298 is an example of such an edit.
In summary, protocol-relative URLs are really common across the MediaWiki namespace on WMF wikis, and will definitely pose a problem when trying to migrate styles to TemplateStyles, and the error message is not of any help."