Well first they would have to see and know why he is a single dad. Is he abusive? Does he strike the child? Is he an alcoholic? Etc., If the single dad is a good guy the society treats him as such. But if he is abusive and that's why he is the single dad probably because he has more money and the mother doesn't than he will be regarded as a loser and a disappointment!! Money isn't everything in this matter!

Typically we do not see single fathers unless the wife is deceased. Even if they won a court battle for custody over the child, they immediately give the child to their parents. So the answer to your question is no one really cares. The child of a single parent lives a more difficult life, most parents will almost abandon the child to save face or not to be shamed, giving them the ability to remarry and live a different life. With most cases when a Chinese mother is a single divorced mother, they live their lives without a real option to remarry unless to a westerner who doesn't see any problem with raising the child. But again, as far as society, no one really cares.

If anything, they will urge the dad to remarry soon so his kids can have a "mother".