Further experimentation yielded another clue. It seems to depend on the position of the mouse pointer. If AbiWord launches in an unmaximized window and the mouse pointer is located outside of that window, the bug behavior happens. If you reposition the mouse pointer, either before opening AbiWord or afterwards, so that the pointer is located in the body of the new document, typing behavior is normal.
Further experimentation yielded another clue. It seems to depend on the position of the mouse pointer. If AbiWord launches in an unmaximized window and the mouse pointer is located outside of that window, the bug behavior happens. If you reposition the mouse pointer, either before opening AbiWord or afterwards, so that the pointer is located in the body of the new document, typing behavior is normal.