Is it ok to exercise with a rotator cuff injury as long as what your doing doesn’t cause pain/discomfort or should you rest it?

It depends on the extent of the injury
I worked out with two torn rotator cuff muscles while waiting for my surgery, I trained everything else and paid extra attention to my motions so as not to aggravate my shoulder
I suggest getting checked out by your doc and a Physical Therapist, then abide by their guidelines.