Here is some debug information on situations where I have seen characters stuck.
I have been suck 2 times. Both times it was after being revived. When it happens, I can't move but can do all other things - use skills, shoot, go into cover, etc. It just seems like the AWSD keys aren't registering.
Fast Traveling to a Safe House tends to fix it. Fast Traveling to the White House doesn't work. Once it is fixed, it doesn't tend to return.
I don't think it has anything to do with network connection or latency but it is hard to know. I don't normally experience latency issues (I have a 1Gb internet connection) to game servers (say ones hosted in AWS) but I haven't measured what it is to any Division2 servers.
Crooth
I had similar issues. After reviving someone I got stuck, but fast traveling didn't fix it. Then last night my whole team got stuck after leaving cover during a mission right in the middle of a big fight. After dying we were all fine and didn't get stuck again. I almost think it might be something to do with lag on the games side. Like the game or server has a hiccup and then we get stuck at odd times. But I might be wrong.