Hint: Going back to 1.3.9 makes it work again.
Connection to the printer established
Nothing / Serial timeout in the console after a few seconds
Yes, safe mode shows the same behavior.
1.3.10rc1
OctoPi 0.14.0
Anycubic Kossel, MKS sBase board, Smoothieware (~ June 2018)
Google Chrome latest, Windows 10 Fall18 Update
https://gist.github.com/zeroflow/1efe8597188962995618d9ca0886fa34
Changing monitoring state from "Offline" to "Detecting serial port"
Serial port list: ['/dev/ttyACM0']
Connecting to: /dev/ttyACM0
Changing monitoring state from "Detecting serial port" to "Opening serial port"
Connected to: Serial
Changing monitoring state from "Opening serial port" to "Connecting"
Connection closed, closing down monitor
Changing monitoring state from "Connecting" to "Offline"

No applicable / or neccesary.
I have read the FAQ.
Can you provide an octoprint.log and serial.log from a working connection attempt under 1.3.9?
Do you have Settings > Serial Connection > Firmware & protocol > Wait for start on connect enabled by any chance?
No, Wait for start on connect is not enabled.
I can reproduce it, the missing start at connection init is the trigger. Shouldn't make stuff stall, but for some reason it does. On it.
Fixed by the above commit, will be part of 1.3.10rc2
1.3.10rc2 was just released.
I can confirm 1.3.10rc2 connects fine to my Klipper printer now (originally reported in #2875).
Most helpful comment
I can confirm 1.3.10rc2 connects fine to my Klipper printer now (originally reported in #2875).