I particularly hate 'pilly' kids clothes (with balls of fluff all over them). Would never judge anyone on the state of their kids clothes ~ maybe their kids a messer, their washing machine is broken, their life is broken and their circumstances are not the best.
My kid is always covered in food, as he's an 11mo self-feeder (read: self-messer).
I always take a spare set of clothes in case of leaking cloth nappy, but won't change him from a food spill unless it's all over him, making him uncomfortable, attracting unwanted attention from the pets, or in polite company.
That said, I think it's sad to see kids with dirty hair/nails and actual sooty residue all over their face and hands. If I do see this (rarely) though, I would feel sorry for the family, talk to the Mum/Dad, and if I can bring it up in a way that doesn't sound too presumptive and it turns out to be circumstancial, will offer use of our facilities/clean clothes etc.
My friend once turned up in middle of winter with her one-week old in singlet suit and top, but no pants or socks. He was freezing (and she wondered why he was not gaining weight...). She declined my offer of some pants for him, so while I was holding him, I took him off and dressed him warmly, and just said I was worried about his gaining weight and wanted to do all I could to assist that.
It's interesting to read how others think about this issue.