Google's John Mueller said that having mixed content on your site and getting mixed content warnings won't result in your site being removed from Google Search. This seems pretty obvious but hey, I don't think I covered this question.
We said previously that the Chrome mixed content notifications do not impact Google Search and that remains true at the time I published this.
John recently said on Twitter "No, mixed content wouldn't result in a site being dropped from search." Here are those tweets:
No, mixed content wouldn't result in a site being dropped from search.
— 🍌 John 🍌 (@JohnMu) February 22, 2021
Google defined mixed content as "when initial HTML is loaded over a secure HTTPS connection, but other resources (such as images, videos, stylesheets, scripts) are loaded over an insecure HTTP connection. This is called mixed content because both HTTP and HTTPS content are being loaded to display the same page, and the initial request was secure over HTTPS." This is super common across the internet currently.
Forum discussion at Twitter.