The protagonist is not able to kill or injure children.
However, children are not immortal.
My compromise would be simple (however, it should be noted that I haven't played the game, so I speak from a general game design principle, not a Skyrim related one)
As I understand it you are supposed to be a hero in Skyrim, and heroes don't kill children unless it is absolutely necessary. However, simply making children immortal is a crude solution.
What about animal attacks, bandit raids, other NPC murderers? If you find a village destroyed by a dragon, but the children are miraculously alive then it would break immersion. However, if you are supposed to be playing a hero, no matter how morally questionable, murdering children is a line that shouldn't be crossed.
It's not about children having the ability to die, it's about wanting to kill children. There is a difference there, and it doesn't seem to be one that gamers can understand. When you want children to be able to die as part of the gaming experience, that's fine. When you want the ability to kill children it's a little different.