Can an employer dictate anything on my Linkedin profile?

Unless you have a contract specifying otherwise, you can be fired for any reason not specifically prohibited by statute (e.g. discrimination on the basis of race, gender, religion, etc., certain types of whistleblowing)  Thus, you can be fired, for example, for calling your boss a hypocrite, even if it was outside of work.  I see no reason why you couldn't be fired for refusing to comply with your employer's linked in policy, again unless you have a contract (could be individual or collectively bargained, could arise from an employee manual) which limits when and/or for what reasons you can be terminated.