This is still happening.
Military phase after giving orders hit advance to next stage. Seems to go fine until it hits the "Political AI is working..." dialog and then it hangs. This last time I left it running while I ran some errands and it was still there an hour and a half later so not just running slower than my patience will allow before killing with Taskmanager
I have sound, music both off.
I have 1.04.3 exe file.
I have all my graphics card settings set to application control.
One thing I think I have noticed is that it happens the 2nd turn if I play two turns in a row. If I just play one turn it's fine.