It's been said before that the Air Nomads had no nonbenders, as they were such a deeply spiritual culture, which is a nice sentiment to explain how Aang would be able to definitely have airbender kids who definitely all have airbender kids etc, but I'm not convinced.
I have a personal theory that there WERE Air Nomad nonbenders, however they were not allowed to remain in the temples. But, it would not be Air-like to suppress a minority, nor for them to be refused to leave. It would be very Air-like to just let them go make their own path, as their own kind of nomad, at an early age. If this is true, then non-airbending people with Air Nomad genes were likely roaming the planet, maybe settling down in cities, etc.
Now while this could have happened, it doesn't really play any relevance. But a separate problem has already arisen as to how Harmonic Convergence had chosen who did and did not get airbending, and I think this theory could answer that. Traditionally the answer has been "all nonbenders", but we only hear from them in the Earth Kingdom, which seems very strange considering that there are plenty of Fire Nation and Water Tribe nonbenders. How come they weren't involved? Some respond to this saying that it's Earth Kingdom nonbenders, as that way, Air is being reborn into its opposite. This would be a fantastic theory if it didn't have a disprove in Bumi. Bumi has an Earth Kingdom name, but otherwise his ancestry is Air Nomad and Water Tribe, so he acts as an exception, thus disproving the rule.
For my theory, the new airbenders are the direct descendants of nonbending nomads left before. As these nomads were out of the temples and had no airbending, the Fire Nation were unable to find or persecute them, and they would likely have no reason to. From an outside perspective, Air Nomads would have all been airbenders after all. Whoever heard of a nonbending Nomad? Allowed to flourish in their own families in the Earth Kingdom, and possibly elsewhere, their descendants now received the gift they did not through their bloodlines. Notably, if nonbenders with airbender ancestry aligns, then it also explains Bumi, a nonbender with an Air Nomad father.