This won’t work well, we warn against clustered/load-balanced setups in the docs. There’s some more details in this topic and a wishlist topic for adding an internal cache adapter which would open up cluster support by externalising the current in-memory caches.
I would suggest using a single instance of Ghost and testing without haproxy. If that works then add the haproxy back in and test again.
Sharing your haproxy config will also help anyone spot any problems. The login issue isn’t reproducible with Safari on standard installs with nginx as the reverse proxy so it sounds like something unique to your environment.