Your problem is the logic you are using the Character Movement component refers to the Character Component instance on the server and not the client instance you have to refer the Character movement component or the Character.
Character 1 on the client might be not Character 1 on the server. Your problem is that you change the variable inside the character component for the server but not for the client and when it tries to replicate movement it jitters between the movement of the client and the servers because they have different walk speeds.
Hope that helps!