...Just to be clear, the browser did not block the site; it just added a warning sign & message, instead of the padlock sign, at the start of the address line.
Understood. What I've seen frequently is that with mixed content (secure and unsecure), the browser can't render a page correctly, till I adjust settings to allow unsecure content. Depending on the website, it can be a subtle effect, or it could be that style elements aren't rendered correctly, and everywhere in between.
I'm reminded now of "Robot Chicken's" spoof of "Tron", both the movie and the video game. As the Main Control Program is under assault, it says, "Computers will rule humans one day! Well, maybe they won't rule humans, just really annoy them!"