It's technically possible, but it would require a very specific context for C to be the natural, correct answer.
The problem is that it does not follow the sequence of tenses. "who were living" is past progressive, so the following verb phrase, "may not appreciate," would also have to occur in the past.
Children who were living in big cities *may not have appreciated...* would be possible.
The meaning of answer C without changing the second verb phrase implies that the children are no longer living in cities, and they still do not appreciate animals. But the reason they do not appreciate animals' company is because they currently live in big cities where few animals are present.