WARNING: Spoilers for Old below.
In Old, the unfortunate people trapped on the cursed beach age rapidly, so why doesn't anyone's hair turn white? The reason behind the quick aging in Old is never explained in full. But the movie eventually offers an explanation as to why their hair and nails don't grow at the same rate as the rest of their bodies and the real reason may be a monetary one.
M. Night Shyamalan's Old follows a group of strangers vacationing at the same resort. The manager offers them the V.I.P treatment and shuttles the group to an exclusive secret beach. What seems idyllic at first eventually turns into terror as the group realizes that they're all aging at an inexplicable and unstoppable rate. Supernatural circumstances stop them from taking the path that would allow them to escape, and the group finds itself in a race against time to figure out a way off the beach before they all die.
Over the course of Old, the characters slowly put the puzzle pieces together, figuring out how much time equates to one year and why they can't leave the beach. One of their initial points is confusion is why their hair doesn't turn white and nails don't grow at a rapid rate. The answer, as one of the group's realizes, is that hair and nails are comprised of dead cells, and the beach's distortion only affects living cells. It's a convenient way of explaining the real (and real-world) issue that's likely behind it: Keeping up with rapidly-changing hair and nails would have cost the Old production team an outrageous amount of money.
In reality, Shyamalan and his team likely just wanted to avoid a massive wig budget. The group in Old eventually deduces that they age one year every half-hour they spend on the beach. So if the movie had victims' hair grow and change at that same rate, the wig budget for the movie would have simply been out of control. The movie would have had to make a handful of realistic-looking wigs for every single character. That would be quite the undertaking to keep up with and if the wigs didn't look absolutely realistic, it would have broken the willing suspension of disbelief. M. Night Shyamalan's solution to avoiding an over-abundance of wigs in Old was a clever one. However, the solution to an unnecessarily expensive problem came with one glaring plothole.
On the surface, Shyamalan's answer to this question makes sense. The vast majority of moviegoers won't have an intensive background in biology. Despite that, the horror film unintentionally created a loophole in its own logic. Early in Old, the unwilling test subjects on the beach discover the body of a dead woman. Judging by the appearance of her body, the group concludes she must have only recently died. After a short amount of time goes by, they take another look at the body and see that it has rapidly decomposed. If the beach's distortion only affects living cells, a dead body should not have decomposed at that rate. In any case, however, the explanation given in Old was still an intriguing one.