Is it ok for cartilage to "pop" in the nose?

This is nothing to be worried about unless you have suffered some trauma and there has been a change in shape and appearance of your nose. The cartilages of the nose tip are not rigidly fixed to each other and therefore any clicking or popping sensation is a normal consequence of them moving against each other.

Popping of the cartilages in the nose specially in the non-operated nose does not significantly point a problem unless there is pain. This sound is caused bu friction between the cartilages such as the lower lateral cartilage and the upper lateral cartilages. The cartilages in the nose are not attached to each other in a rigid manner making  some movement possible. Don't consider it a disorder.
Hope this helps,
Ali Rıza Öreroğlu, MD FEBOPRASEuropean and Turkish Board Certified Aesthetic, Plastic and Reconstructive SurgeonIstanbul, Turkey

This is not too uncommon as the cartilage is not rigidly fixed and can move around from time to time. As long as it's not causing any pain or problems it's nothing to worry about.

Some people experience clicking in the nasal base after rhinoplasty, and occasionally some feel clicking or popping as your lower lateral cartilages are moved past the bottom of your nasal septum. If all else is fine with your nose, this should not be a significant issue. Consider consulting with a rhinoplasty specialist for an evaluation. Hope this helps! Dr Joseph

This is normal, and can happen to someone who has never had a rhinoplasty, or individuals who have had surgery of some type on their nose.  Regardless, if it is something you are worried about, always best to have it checked out by a professional in the field.