The information is from a BBC News article referencing Google's Chrome Development website. Whilst it may only initially refer to Chrome, it is almost certain that other browser creators will be interested to see what develops.
BBC News - Google considers warning internet users about data risks
Marking HTTP As Non-Secure - The Chromium Projects
I do appreciate that Muse is only an application to create a website without having to learn html, however I was thinking of the whole Business Catalyst / Muse as a package and what may develop, if and when Google's proposal takes off. I that case would Business Catalyst offer an option to purchase or subscribe to a security certificate.