For at least some keys, reassignments are not respected for all functions. I am left handed and have the WASD movement keys reassigned to the arrow keys. I also have "E", the default for activate or use, reassigned to "DELETE" on the nav keypad to be near the arrow keys. "DELETE" works for some activate functions, but not others. For example, taking items from dead NPC's still requires the "E" key even though it has been reassigned.
Early in the game, I came across a function requiring directional input and couldn't get the arrow keys to work. Turns out I needed to revert to the WASD keys. I can't now remember what it was since I haven't encountered it again. However, a new related instance makes the game unplayable to me. I'm on the "Old Guns" quest, where for the first time I have to assign an NPC to a given task. Once I engage the NPC and give it the assignment command, I'm supposed to move to the item to be assigned. At this point, the arrows keys will not work and I cannot move. The WASD keys don't work either. The only workaround is to reset the key assignments to the default configuration and use the WASD keys for movement.
This needs to be fixed for lefties. Dropping the key assignments for every NPC assignment and then having to reset the dropped keys in not viable in when it has to be done multiple times to set up settlements, It's gotten to the point that I have stopped playing until this bug gets fixed.