Whether your manager is interested in your welfare or not, if you are interested in trying to protect your current job (or maximise the opportunity to extract money if you are forced to leave through redundancy or unfair dismissal) I suggest you consider doing something of this sort. And your line manager is the right place to start the process - you are employed by the company, not your manager, so it is the corporate entity that has to ensure it follows a reasonable set of procedures, from your disgruntled manager upwards.
Singling-out part-timers for dismissal (redundancy?) solely because they are part-timers generally is unfair; contract workers unfortunately would be expected to be the ones to be shifted in any downsizing.