This is my 6th month after my shoulder dislocated. can i perform bodyweight parallel dips and chin-ups?

Depends : It depends on if you made a full recovery. Most patients who have had a simple shoulder dislocation without complication can return to full activities by 12 weeks. Some patients who dislocate their shoulders may have torn some ligaments and other structures that may not completely heal and need to be careful or have something further done. An exam can usually determine this. Thank you.

Maybe maybe not: Start out slowly and do not reinjure the shoulder by 6 mo it should be pretty well healed but a 6 mo time out of exercise will mean you need to gradually ramp up your activity once dislocated there is always an increased risk of redislcoation.