I recently upgraded to Little Snitch 4.0.3 on my MacBook Pro (Mid-2012) running Mac OS 10.12.6. After installation and reboot of the MacBook Pro, I experienced a number of random issues.
On entering the password for my user account, I would be returned to the login. Restarting in safe mode (holding the SHIFT key on boot) finally allowed me to login screen.
Finder would crash and re-open automatically
Safari would crash
The wallpaper did not load
The top menu bar would not load
I removed Little Snitch (4.0.3) using AppZapper and rebooted which seemed to work. Then after some research on the forums, I decided to attempt a re-install of Little Snitch. The issues repeated itself consistently. I've gotten to this point by rebooting the MacBook Pro and holding COMMAND+OPTION+R for recovery mode. I was able to login and entered my license key for Little Snitch. Things look okay but I'm hesitant to do a reboot to see what will happen.
I have two SSD in RAID 0, Trim Enabler and 16GB of memory. If there is anything else that you would need to know to help in diagnosing this issue please don't hesitate to ask. I like this app but not when it put my MacBook Pro at risk.