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. 

It sounds like you haven't had nose surgery, but either way it can be normal for the nasal cartilage to rub and pop at times. You can have the area checked out by an otolaryngologist (ear nose throat doctor) or facial plastic surgeon if you're concerned about something else going on.

Plenty of normal noses that have never had any surgery can create a clicking or popping sound or sensation when moving the tip of the nose around, as the lower lateral cartilages can slide and move against each other and create that sound. Unless you had a recent trauma with a change in the appearance of your nose, or are having pain, I would not worry. Otherwise feel free to meet with a plastic surgeon for further evaluation.
-David Mattos, Harvard-trained plastic surgeon

Nasal popping or crunching is quite common and is caused by the upper and lower lateral cartilages creating friction with each other during movement. If there is pain associated with your concern, you should schedule an appointment with a nasal specialist. Additional signs of nasal damage tend to be bruising, cosmetic differences and breathing problems. A rhinoplasty surgeon will assess your condition and evaluate whether the nasal popping is due to displaced cartilage or not. 

 Popping of cartilage in the nose is normal, and that's usually just related to the upper lateral cartilages  and the lower lateral colleges rubbing against each other. It's nothing to worry about and  surgery will not improve it.  Digital computer imaging would be helpful to understand what can be accomplished with a rhinoplasty procedure.  For many examples of surgical  closed rhinoplasty to change the shape of the nose, please see the link and the video below

Don't worry about popping and clicking noises in the tip. Your cartilage is probably sliding over another cartilage (like the septum or upper lateral cartilage). As long as your nose is not bleeding or swelling, it sounds pretty normal. If you are worried, see an otolaryngologist (ENT) or facial plastic surgeon.