I am playing on a PC and purchased the game from GOG. This is happening on the Definitive Edition. It happens when using the GOG interface to open the game AND when I open the game directly. The bug was noticed at the beginning of February 2019. There was another movement bug (Mobs not moving when they lost LOS) that happened at the same time. As such, I waited to see if the fix to that bug would fix this one as well. It didn't.
I send a character to go somewhere and if that character is deselected for any reason it immediately stops. I haven't seen any posts in updates that indicated this change. Basically only 1 selected character or group of characters can be moving at a time. To be specific, if I have multiple groups of characters, I can only move one at a time. If I start a dialog and then want to move an unchained character or group of characters I can do this. However, as soon as I select the character in dialog, the group that was moving immediately stops. The same happens if I want to move 2 unchained groups at the same time. As soon as a different group is selected, the other group stops. This happens when using the mouse or keys (F1, F2, F3, F4) to switch to a different group. This makes positioning tactically for a combat take quite a bit more time.
