The current title of this post (”Chrome 44 breaks any wordpress site not able to serve in HTTPS”) seems exaggerated.
This issue does not render all non-HTTPS WP sites useless. I tried on a friend’s site and it served fine in Chrome version 44.0.2403.89.
After skimming the bug report it seems to mostly affect the login functionality and not the user-facing parts of WP. Still problematic but less severe than what it sounds like.