Not much help but I'm seeing the exact same issue.
No nothing, both machines are installed clean with the latest version of Civ V with nothing other added than this mod.
Let me know if and want you need from me to debug.
I installed the 5.21 and tried to run it in MP but after each turn I get the loading screen on both PC's, is that normal?
Would it be possible to add EUI, there are functions in there that are pretty handy
Separate names with a comma.