In short, yes, tone deafness is a genuine neurological disorder. It's called amusia. However, not everyone who lacks musical skills has this condition, which affects an estimated 4% of the population (opens in new tab).
https://www.livescience.com/human-behavior/are-some-people-actually-tone-deaf #amusia #ToneDeaf
Are some people actually tone deaf?

Tone deafness, a neurological disorder known as amusia, can make it hard to distinguish between musical pitches.

Live Science