Screen Sharing is working on LAN but Macs can't connect
I have two Macs on a wired network both running macOS Sierra, a MBP and a iMac.
Both are set in sharing preferences for File, Screen and Internet sharing. I have been sharing them on this ethernet network for years. About a month ago this changed.
Now, I can share the iMac's screen from the MBP but cannot connect as a Registered User. I get the interface "shake" which I presume means incorrect password. However, screen sharing just goes straight through so how can this be?
Going the other way, I get the same "shake" when I log into the MBP from the iMac. However, screen sharing is not offered as an option, even though the system preferences are set for this.
If I disconnect the Ethernet and run the network wirelessly I get exactly the same results.
The only connection blocking program that I'm knowingly running is Little Snitch. Switching that off on both computers doesn't change the outcome.
Any idea what I need to do to get the network working fully again?
iMac, macOS 10.12