I've just set up CloudFlare for my website, so that I can run HTTPS (yes, I know it's not encrypted end-to-end... this is fine). All the images, script resources, etc. are now linked using protocol-agnostic URLs, but I'm still not getting the green 'Secure' indicator in Chrome's address bar.
This is because Blogger is injecting their nav/header bar into my pages, and that bar includes a search form with an
action attribute of "http://www.example.com/" (no HTTPS)
I can't use CloudFlare to rewrite it because it's not being served from my own host. I've tried hiding it using CSS but this doesn't remove the warning. There's no explicit option I can find anywhere in the Blogger admin to configure or remove this header/search bar.