You can use Input.ResetInputAxes() every frame that you're typing, though that doesn't work too well if you're using FixedUpdate - it'll still move every so often (when there is more than one fixedupdate in a frame)
Better way would be to store that you're typing, and your other scripts to check with a static bool somewhere for if they're allowed to move
You can apply the same kind of logic to button presses. You just need to check to see if your text field has focus, and if so early out of your key input events.