This isn't going to be good. There are going to be people who are unaware of the incompatibility and upgrade to Mojave, and then be left with Synergy nonfunctional.
It would be nice to get a comment from Symless as to whether a fix is even being worked on.
I GOT IT WORKING!!
There appears to be an issue when "Enable Auto Config" is disabled.
Here's what I did (macOS Mojave is Server):
I followed the steps to reinstall from fresh
Removed the app from System Preferences' "Security & Privacy > Accessibility" list
Opened the app
From System Preferences, I enabled Accessibility access, as requested
Back in Synergy, enabled Auto Config (in Preferences, picture below)
Allowed my client (Windows 1